The vertices of the 1 cm side are cut from each corner of a square with a side of 4.5 cm. Find the circumference and area of the octagon formed?

$$ {5 sqrt{2}}{ cm};{18.25{ cm^{2}}}$$

$$ {(5+4 sqrt{2})}{ cm}; {18.25 cm^{2}}$$

$$ {(10+4 sqrt{2})}{ cm}; {18.25 cm^{2}}$$

The perimeter of an isosceles, right angled triangle is 2p unit. The area of the same triangle is

$$ {(2+ sqrt{2})}{ p^{2}} sq.unit $$

$$ {(3-2 sqrt{2})}{ p^{2}} sq.unit $$

$$ {(2+ sqrt{2})}{ p^{2}} sq.unit $$

$$ {(2- sqrt{2})}{ p^{2}} sq.unit $$

$$ {(3- sqrt{2})}{ p^{2}} sq.unit $$

151 + Mcqs in Volume and Surface Area Questions in Maths Page 1 McqOptions

1.	The height of a cone is 16 cm and radius of its base is 30 cm. If the rate of painting it is Rs.14/cm², then what will be the total cost in painting the curved surface of cone from outside?
A.	Rs. 42220
B.	Rs. 44880
C.	Rs. 36820
D.	Rs.46540
Answer» C. Rs. 36820

Discussion

2.	The slant height of a right circular cone is 15 m and its height is 9 m. The area of its curved surface, is:
A.	169 m2
B.	172 m2
C.	165 m2
D.	180 m2
Answer» E.

Discussion

3.	The volume of a solid right circular cylinder is 5236 cm³, and its height is 34 cm. What is its curved surface area (in cm²)?
A.	1496
B.	1573
C.	1650
D.	1804
Answer» B. 1573

Discussion

4.	A conical vessel whose internal base radius is 18 cm and height 60 cm is full of a liquid. The entire liquid of the vessel is emptied into a cylindrical vessel with internal radius 15 cm. The height (in cm) to which the liquid rises in the cylindrical vessel is:
A.	30.2 cm
B.	28.8 cm
C.	27 cm
D.	24 cm
Answer» C. 27 cm

Discussion

5.	The length, breadth and height of a room is 21 metres, 12 metres and 16 metres. What will be the length of the largest rod that can be placed in that room?
A.	32 metres
B.	25 metres
C.	31 metres
D.	29 metres
Answer» E.

Discussion

6.	The diagonals of a rhombus are 24 cm. and 10 cm. The perimeter (in cm) of this rhombus is-
A.	54
B.	68
C.	52
D.	54
Answer» D. 54

Discussion

7.	Find the volume of the material in a cylindrical tube. The radius of the outer surface being 10 m, the thickness being 0.4 m and the height being 9 m.
A.	$$ {224 {m^{3}}}$$
B.	$$ {224 {m^{3}}}$$
C.	None of these
D.	$$ {229 {m^{3}}}$$
E.	$$ {218 {m^{3}}}$$
Answer» D. $$ {229 {m^{3}}}$$

Discussion

8.	Three solid metallic sphere whose radii are 3cm, x cm and 18cm respectively, are melted and recast into a single solid sphere of diameter 38cm. Then find the total surface area of the sphere with radius x cm?
A.	300
B.	400
C.	100
D.	200
Answer» C. 100

Discussion

9.	A field is in the form of an equilateral triangle of side 100 m. A horse is tied to a vertex of the field, with a 15 m long rope. Over what area can the horse graze?
A.	117.85 m
B.	119.85 m
C.	117.35 m
D.	119.35 m2
Answer» B. 119.85 m

Discussion

10.	A rectangular grass plot 80 m 60 m has two roads, each 10 m wide, running in the middle of it; one parallel to length and the other parallel to breadth. Find the cost of gravelling the roads at 2 per m².
A.	2600
B.	2680
C.	2580
D.	2500
Answer» B. 2680

Discussion

11.	A shuttlecock used of playing badminton has the shape of a frustum of a cone mounted on a semi sphere. The external diameters of the frustum are 5 cm and 2 cm, the height of the entire shuttlecock is 7 cm. The external surface is of the shuttlecock is:
A.	67.98 sq.cm
B.	74.26 sq.cm
C.	70 sq.cm
D.	72 sq.cm
Answer» C. 70 sq.cm

Discussion

12.	A cylindrical container is filled with ice cream. Its diameter is 12 cm. and height is 15 cm. The whole ice cream is distributed among 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, the diameter of the ice - cream cone is
A.	8 cm
B.	5 cm
C.	7 cm
D.	6 cm
Answer» E.

Discussion

13.	A corner of a cube of side length 8 m. When cut by a plane which bisects the sides of the cube, we get a pyramid whose volume is :
A.	8.37 m3
B.	10.67 m3
C.	11.20 m3
D.	9.68 m3
Answer» C. 11.20 m3

Discussion

14.	A conical vessel of radius 6 cm and height 8 cm. is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. The fraction of water that overflows is?
A.	$$ {1 over 4}$$
B.	$$ {1 over 2}$$
C.	$$ {3 over 8}$$
D.	$$ {5 over 8}$$
Answer» D. $$ {5 over 8}$$

Discussion

15.	Area of a rectangle is equal to the area of a circle whose radius is 14 cm. If the breadth of the rectangle is 22 cm, what is its length?
A.	24 cm
B.	28 cm
C.	26 cm
D.	Cannot be determined
E.	None of these
Answer» C. 26 cm

Discussion

16.	By increasing the radius of a sphere by 50 percent, how much will the area of its surface increase?
A.	100%
B.	125 %
C.	150%
D.	None of these
Answer» C. 150%

Discussion

17.	The base of right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1731.6 cm³, then the height (in cm) of the prism will be:
A.	15.2
B.	14.8
C.	15.6
D.	14.2
Answer» C. 15.6

Discussion

18.	The areas of the three adjacent faces of a cuboid are 32 cm², 24 cm² and 48cm². What is the volume of the cuboid?
A.	288 cm3
B.	256 cm3
C.	128 cm3
D.	192 cm3
Answer» E.

Discussion

19.	A hollow copper pipe is 22 cm long and its external diameter is 28 cm. If the thickness of the pipe is 3 cm and iron weighs 8.5 g/cm³ , then the weight of the pipe is closest to:
A.	34 kg
B.	44 kg
C.	14 kg
D.	24 kg
Answer» C. 14 kg

Discussion

20.	A wall is the form of a trapezium with height 8 m and parallel sides being 5 m and 10 m. What is the cost of painting the wall, if the rate of painting is Rs. 50 per square meter ?
A.	Rs.5000
B.	Rs.3000
C.	Rs.6000
D.	Rs .4000
Answer» C. Rs.6000

Discussion

21.	What is the area of an equilateral triangle having altitude equal to $$5 sqrt{3}$$cm.
A.	$$25 sqrt{3}$$
B.	$$45 sqrt{3}$$
C.	45
D.	40
Answer» B. $$45 sqrt{3}$$

Discussion

22.	In a circle, difference between the circumference and radius is 37 cm. Find the area (in cm ) of the circle?
A.	616
B.	154
C.	308
D.	77
Answer» C. 308

Discussion

23.	The perimeter of a circle is equal to the square perimeter. What will be the ratio of their areas?
A.	4 : 1
B.	11 : 7
C.	14:11
D.	11:14
Answer» D. 11:14

Discussion

24.	The ratio of the areas of two circles is 16: 25. What will be the ratio of their circumferences?
A.	4 : 5
B.	3 : 2
C.	4 : 9
D.	9 : 4
Answer» B. 3 : 2

Discussion

25.	The measure of a cuboid warehouse is (8 m x 6 m x 3 m). If each sack covers 0.48 cubic meters of space, how many maximum sacks can be kept in it?
A.	221
B.	300
C.	320
D.	None of these
Answer» C. 320

Discussion

26.	If the length of the diagonal of a square is $${ 10 sqrt{2}}$$ cm, then what will be the area of the square?
A.	200 cm2
B.	100 cm2
C.	$$ {100}{ sqrt{2} $ cm2
D.	50 cm2
Answer» C. $$ {100}{ sqrt{2} $ cm2

Discussion

27.	A polygon has 9 sides, what is its interior angle?
A.	140 degree
B.	100 degree
C.	120 degree
D.	40 degree
Answer» B. 100 degree

Discussion

28.	The vertices of the 1 cm side are cut from each corner of a square with a side of 4.5 cm. Find the circumference and area of the octagon formed?
A.	$$ {5 sqrt{2}}{ cm};{18.25{ cm^{2}}}$$
B.	$$ {(5+4 sqrt{2})}{ cm}; {18.25 cm^{2}}$$
C.	$$ {(10+4 sqrt{2})}{ cm}; {18.25 cm^{2}}$$
D.	16 cm and 16 sq.cm
Answer» D. 16 cm and 16 sq.cm

Discussion

29.	The curved surface area of a right circular cylinder of radius 2 cm is 264 cm². The height of the cylinder, in cm, is
A.	42
B.	14
C.	10.5
D.	21
Answer» E.

Discussion

30.	Base of a right pyramid is a square. The length of diagonal of the base is $$ {12 sqrt{2}}$$ cm. If each lateral surface of the pyramid is an equilateral triangle, then its volume (in cu.cm) is
A.	$$ {288 sqrt{3}}$$
B.	$$ {208 sqrt{2}}$$
C.	$$ {288 sqrt{2}}$$
D.	288
Answer» B. $$ {208 sqrt{2}}$$

Discussion

31.	The perimeter of a rectangle and equilateral triangle is equal. One side of the rectangle is also equal to the side of the triangle. Find the ratio of the areas of the rectangle and triangle?
A.	$$ { sqrt{3}:1}$$
B.	$$ {1 : sqrt{3}}$$
C.	$$ {2 : sqrt{3}}$$
D.	$$ {4 : sqrt{3}}$$
Answer» D. $$ {4 : sqrt{3}}$$

Discussion

32.	Two 6 cm diameter balls dipped in a 6 cm radius cylindrical vessel of water. Find the height of water in the vessel?
A.	1 cm
B.	2 cm
C.	3 cm
D.	4 cm
Answer» C. 3 cm

Discussion

33.	How much parts of the pits, which are 48 meters long, 16.5 meters wide and 4 meters deep, can be filled in the soil, which is obtained by cylindrical tunnel of 4 meters diameter and 56 meters long?
A.	$$ {1 over 9}$$
B.	$$ {2 over 9}$$
C.	$$ {7 over 9}$$
D.	$$ {8 over 9}$$
Answer» C. $$ {7 over 9}$$

Discussion

34.	The edges of a cuboid are in the ratio 1 : 2: 3 and its surface area is 88 sq.cm. The volume of the cuboid is:
A.	24
B.	48
C.	64
D.	120
Answer» C. 64

Discussion

35.	If the curved surface area of a right circular cone is 10010 sq cm and its slant height is 91 cm, nd its total surface area.
A.	27720 sq cm
B.	4620 sq cm
C.	6930 sq cm
D.	13860 sq cm
Answer» E.

Discussion

36.	A conical vessel whose internal radius is 12 cm and height 50 cm. is full of liquid. The contents are emptied into a cylindrical vessel with radius (internal) 10 cm. The height to which the liquid rises in the cylindrical vessel is-
A.	25 cm
B.	20 cm
C.	24 cm
D.	22 cm
Answer» D. 22 cm

Discussion

37.	Area of a circle inscribed in a square is 308 cm².The length of the diagonal of the square is
A.	16 cm
B.	28 cm
C.	24 cm
D.	22 cm
Answer» C. 24 cm

Discussion

38.	The ratio of the areas of two isosceles triangles having the same vertical angle is 1 : 9.The ratio of their heights is -
A.	1 : 3
B.	1 : 9
C.	3 : 1
D.	1 : 81
Answer» B. 1 : 9

Discussion

39.	If a chord of length 30 cm is at a distance of 8 cm from the center of the circle, then the length of the chord of the same circle which is at a distance of 15 cm from the center is equal to
A.	12 cm
B.	18 cm.
C.	16 cm
D.	20 cm.
Answer» D. 20 cm.

Discussion

40.	If the areas of circular ring having inner and outer radius 8 cm and 12 cm respectively is equal to the total surface area of cylinder of radius R₁and height h, then h in terms of R₁ will be :
A.	$$ {40-R_1 over {R_1}}$$
B.	$$ {40-R_1 over {R_1^{2}}}$$
C.	$$ {40-R_1^{2}} over R_1$$
D.	None of these
Answer» D. None of these

Discussion

41.	The perimeter of an isosceles, right angled triangle is 2p unit. The area of the same triangle is
A.	$$ {(3-2 sqrt{2})}{ p^{2}} sq.unit $$
B.	$$ {(2+ sqrt{2})}{ p^{2}} sq.unit $$
C.	$$ {(2- sqrt{2})}{ p^{2}} sq.unit $$
D.	$$ {(3- sqrt{2})}{ p^{2}} sq.unit $$
Answer» B. $$ {(2+ sqrt{2})}{ p^{2}} sq.unit $$

Discussion

42.	Find the area of triangle whose medians are 8 cm, 15 cm and 17 cm respectively?
A.	$$20 cm^2$$
B.	$$15 cm^2$$
C.	$$24 cm^2$$
D.	$$28 cm^2$$
Answer» B. $$15 cm^2$$

Discussion

43.	A solid metallic cylinder of base radius 3 cm. and height 5 cm. is melted to form cones, each of height 1 cm. and base radius 1 mm. The number of cones is -
A.	12540
B.	13500
C.	24400
D.	11600
Answer» C. 24400

Discussion

44.	A regular hexagon has a side of 4 cm. Find its area. (in sq. cm)
A.	$$ {24 sqrt{3}}$$
B.	$$ {18 sqrt{3}}$$
C.	$$ {36 sqrt{3}}$$
D.	None of these
Answer» B. $$ {18 sqrt{3}}$$

Discussion

45.	If the ratio of the areas of two similar triangle ABC and DEF is 36:81 and EF = 6.9 cm., then BC is equal to
A.	4.6 cm.
B.	6.4 cm.
C.	4 cm.
D.	6 cm.
Answer» B. 6.4 cm.

Discussion

46.	In a circle of radius 17 cm, two parallel chords of lengths 30 cm. and 16 cm are drawn. If both the chords are on the same side of the center, then the distance between the chords is -
A.	7 cm.
B.	17 cm.
C.	9 cm.
D.	23 cm.
Answer» B. 17 cm.

Discussion

47.	The lengths of the parallel sides of a trapezium are 51 cm and 21 cm, and that of each of the other two sides is 39 cm. what is the area ( in cm²) of the trapezium?
A.	1206
B.	1152
C.	1260
D.	1296
Answer» E.

Discussion

48.	The perimeter of a square and an equilateral triangle is the same if the length of the diagonal of the square is $$ {12 sqrt {2}} $$ cm. If, what will be the area of the triangle?
A.	$$ {64 sqrt{3}}$$ sq.cm
B.	$$ {32 sqrt{3}}$$ sq.cm
C.	$$ {24 sqrt{3}}$$ sq.cm
D.	$$ {28 sqrt{3}}$$ sq.cm
Answer» B. $$ {32 sqrt{3}}$$ sq.cm

Discussion

49.	From a right cone of height h and with base radius r a cone has been cut of from the centre of the height. The volume of remaining frustum of the cone is.
A.	$$ {1 over3} {r^{2}}h$$
B.	$$ {1 over24} {r^{2}}h$$
C.	$$ {7 over24} {r^{2}}h$$
D.	$$ {1 over8} {r^{2}}h$$
Answer» D. $$ {1 over8} {r^{2}}h$$

Discussion

50.	A straight line parallel to the base QR of the PQR intersect PQ and PR at the points S and T respectively. If the area of the PQT be 36 cm² then area of the PRS is:
A.	$$ {18 { cm^{2}}}$$
B.	$$ {36 { cm^{2}}}$$
C.	$$ {28 { cm^{2}}}$$
D.	$$ {48 { cm^{2}}}$$
Answer» C. $$ {28 { cm^{2}}}$$

Discussion

Explore topic-wise MCQs in Maths.

The height of a cone is 16 cm and radius of its base is 30 cm. If the rate of painting it is Rs.14/cm2, then what will be the total cost in painting the curved surface of cone from outside?

The slant height of a right circular cone is 15 m and its height is 9 m. The area of its curved surface, is:

The volume of a solid right circular cylinder is 5236 cm3, and its height is 34 cm. What is its curved surface area (in cm2)?

A conical vessel whose internal base radius is 18 cm and height 60 cm is full of a liquid. The entire liquid of the vessel is emptied into a cylindrical vessel with internal radius 15 cm. The height (in cm) to which the liquid rises in the cylindrical vessel is:

The length, breadth and height of a room is 21 metres, 12 metres and 16 metres. What will be the length of the largest rod that can be placed in that room?

The diagonals of a rhombus are 24 cm. and 10 cm. The perimeter (in cm) of this rhombus is-

Find the volume of the material in a cylindrical tube. The radius of the outer surface being 10 m, the thickness being 0.4 m and the height being 9 m.

Three solid metallic sphere whose radii are 3cm, x cm and 18cm respectively, are melted and recast into a single solid sphere of diameter 38cm. Then find the total surface area of the sphere with radius x cm?

A field is in the form of an equilateral triangle of side 100 m. A horse is tied to a vertex of the field, with a 15 m long rope. Over what area can the horse graze?

A rectangular grass plot 80 m 60 m has two roads, each 10 m wide, running in the middle of it; one parallel to length and the other parallel to breadth. Find the cost of gravelling the roads at 2 per m2.

A shuttlecock used of playing badminton has the shape of a frustum of a cone mounted on a semi sphere. The external diameters of the frustum are 5 cm and 2 cm, the height of the entire shuttlecock is 7 cm. The external surface is of the shuttlecock is:

A corner of a cube of side length 8 m. When cut by a plane which bisects the sides of the cube, we get a pyramid whose volume is :

A conical vessel of radius 6 cm and height 8 cm. is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. The fraction of water that overflows is?

Area of a rectangle is equal to the area of a circle whose radius is 14 cm. If the breadth of the rectangle is 22 cm, what is its length?

By increasing the radius of a sphere by 50 percent, how much will the area of its surface increase?

The base of right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1731.6 cm3, then the height (in cm) of the prism will be:

The areas of the three adjacent faces of a cuboid are 32 cm2, 24 cm2 and 48cm2. What is the volume of the cuboid?

A hollow copper pipe is 22 cm long and its external diameter is 28 cm. If the thickness of the pipe is 3 cm and iron weighs 8.5 g/cm3 , then the weight of the pipe is closest to:

A wall is the form of a trapezium with height 8 m and parallel sides being 5 m and 10 m. What is the cost of painting the wall, if the rate of painting is Rs. 50 per square meter ?

What is the area of an equilateral triangle having altitude equal to $$5 sqrt{3}$$cm.

In a circle, difference between the circumference and radius is 37 cm. Find the area (in cm ) of the circle?

The perimeter of a circle is equal to the square perimeter. What will be the ratio of their areas?

The ratio of the areas of two circles is 16: 25. What will be the ratio of their circumferences?

The measure of a cuboid warehouse is (8 m x 6 m x 3 m). If each sack covers 0.48 cubic meters of space, how many maximum sacks can be kept in it?

If the length of the diagonal of a square is $${ 10 sqrt{2}}$$ cm, then what will be the area of the square?

A polygon has 9 sides, what is its interior angle?

The vertices of the 1 cm side are cut from each corner of a square with a side of 4.5 cm. Find the circumference and area of the octagon formed?

The curved surface area of a right circular cylinder of radius 2 cm is 264 cm2. The height of the cylinder, in cm, is

Base of a right pyramid is a square. The length of diagonal of the base is $$ {12 sqrt{2}}$$ cm. If each lateral surface of the pyramid is an equilateral triangle, then its volume (in cu.cm) is

The perimeter of a rectangle and equilateral triangle is equal. One side of the rectangle is also equal to the side of the triangle. Find the ratio of the areas of the rectangle and triangle?

Two 6 cm diameter balls dipped in a 6 cm radius cylindrical vessel of water. Find the height of water in the vessel?

How much parts of the pits, which are 48 meters long, 16.5 meters wide and 4 meters deep, can be filled in the soil, which is obtained by cylindrical tunnel of 4 meters diameter and 56 meters long?

The edges of a cuboid are in the ratio 1 : 2: 3 and its surface area is 88 sq.cm. The volume of the cuboid is:

If the curved surface area of a right circular cone is 10010 sq cm and its slant height is 91 cm, nd its total surface area.

A conical vessel whose internal radius is 12 cm and height 50 cm. is full of liquid. The contents are emptied into a cylindrical vessel with radius (internal) 10 cm. The height to which the liquid rises in the cylindrical vessel is-

Area of a circle inscribed in a square is 308 cm2.The length of the diagonal of the square is

The ratio of the areas of two isosceles triangles having the same vertical angle is 1 : 9.The ratio of their heights is -

If a chord of length 30 cm is at a distance of 8 cm from the center of the circle, then the length of the chord of the same circle which is at a distance of 15 cm from the center is equal to

If the areas of circular ring having inner and outer radius 8 cm and 12 cm respectively is equal to the total surface area of cylinder of radius R1 and height h, then h in terms of R1 will be :

The perimeter of an isosceles, right angled triangle is 2p unit. The area of the same triangle is

Find the area of triangle whose medians are 8 cm, 15 cm and 17 cm respectively?

A solid metallic cylinder of base radius 3 cm. and height 5 cm. is melted to form cones, each of height 1 cm. and base radius 1 mm. The number of cones is -

A regular hexagon has a side of 4 cm. Find its area. (in sq. cm)

If the ratio of the areas of two similar triangle ABC and DEF is 36:81 and EF = 6.9 cm., then BC is equal to

In a circle of radius 17 cm, two parallel chords of lengths 30 cm. and 16 cm are drawn. If both the chords are on the same side of the center, then the distance between the chords is -

The lengths of the parallel sides of a trapezium are 51 cm and 21 cm, and that of each of the other two sides is 39 cm. what is the area ( in cm2) of the trapezium?

The perimeter of a square and an equilateral triangle is the same if the length of the diagonal of the square is $$ {12 sqrt {2}} $$ cm. If, what will be the area of the triangle?

From a right cone of height h and with base radius r a cone has been cut of from the centre of the height. The volume of remaining frustum of the cone is.

A straight line parallel to the base QR of the PQR intersect PQ and PR at the points S and T respectively. If the area of the PQT be 36 cm2 then area of the PRS is:

The height of a cone is 16 cm and radius of its base is 30 cm. If the rate of painting it is Rs.14/cm², then what will be the total cost in painting the curved surface of cone from outside?

The volume of a solid right circular cylinder is 5236 cm³, and its height is 34 cm. What is its curved surface area (in cm²)?

A rectangular grass plot 80 m 60 m has two roads, each 10 m wide, running in the middle of it; one parallel to length and the other parallel to breadth. Find the cost of gravelling the roads at 2 per m².

The base of right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1731.6 cm³, then the height (in cm) of the prism will be:

The areas of the three adjacent faces of a cuboid are 32 cm², 24 cm² and 48cm². What is the volume of the cuboid?

A hollow copper pipe is 22 cm long and its external diameter is 28 cm. If the thickness of the pipe is 3 cm and iron weighs 8.5 g/cm³ , then the weight of the pipe is closest to:

The curved surface area of a right circular cylinder of radius 2 cm is 264 cm². The height of the cylinder, in cm, is

Area of a circle inscribed in a square is 308 cm².The length of the diagonal of the square is

If the areas of circular ring having inner and outer radius 8 cm and 12 cm respectively is equal to the total surface area of cylinder of radius R₁and height h, then h in terms of R₁ will be :

The lengths of the parallel sides of a trapezium are 51 cm and 21 cm, and that of each of the other two sides is 39 cm. what is the area ( in cm²) of the trapezium?

A straight line parallel to the base QR of the PQR intersect PQ and PR at the points S and T respectively. If the area of the PQT be 36 cm² then area of the PRS is: