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Use `pi=22/7`
किसी बाल्टी की ऊंचाई 45 सेमी. तथा दोनों सिरो की त्रिज्याऐं क्रमशः 28 सेमी. तथा 7 सेमी. है। बाल्टी का आयतन ज्ञात करें?
A. 48510
B. 45810
C. 48150
D. 48051
Correct Answer - AVolume of bucket `=1/3pih(R^(2)+r^(2)+Rr)` `=1/3xx22/7xx45(28^(2)+7^(2)28xx7)` `=22/7xx15xx1029=48510cm^(3)`
Correct Answer – A
See lessVolume of bucket
`=1/3pih(R^(2)+r^(2)+Rr)`
`=1/3xx22/7xx45(28^(2)+7^(2)28xx7)`
`=22/7xx15xx1029=48510cm^(3)`
The sum of the squares of the sides of a rhombus is 900 m2. What is the side of the rhombus.
1. 16 m
2. 15 m
3. 14 m
4. 17 m
Correct Answer - Option 2 : 15 mGiven:4(side of rhombus)2 = 900 m2Concept:The side of a rhombus is equal.Calculation:Let the side of the rhombus 'a'∴ Sum of side of Rhombus = 4a∵ 4a2 = 900 m2⇒ a2 = 900/4 m2⇒ a = √(900/4) m⇒ a = 30/2 m⇒ a = 15 m
Correct Answer – Option 2 : 15 m
Given:
4(side of rhombus)2 = 900 m2
Concept:
The side of a rhombus is equal.
Calculation:
Let the side of the rhombus ‘a’
∴ Sum of side of Rhombus = 4a
∵ 4a2 = 900 m2
⇒ a2 = 900/4 m2
⇒ a = √(900/4) m
⇒ a = 30/2 m
⇒ a = 15 m
See lessCurved surface area of a cylinder is 308 cm2, and height is 14 cm. What will be the volume of the cylinder?
1. 439 cm3
2. 385 cm3
3. 539 cm3
4. 529 cm3
Correct Answer - Option 3 : 539 cm3Given:Curved surface area of cylinder = 308 cm2Height = 14 cmFormula used:CSA (Curved surface area) = 2πrhVolume = πr2hWhere r is radius and h is heightCalculation:CSA = 2πrh308 = 2 × (22/7) × r × 14⇒ 308 = 88r⇒ r = 7/2 = 3.5 cmVolume = πr2h⇒ Volume = (22/7) × (3.5Read more
Correct Answer – Option 3 : 539 cm3
Given:
Curved surface area of cylinder = 308 cm2
Height = 14 cm
Formula used:
CSA (Curved surface area) = 2πrh
Volume = πr2h
Where r is radius and h is height
Calculation:
CSA = 2πrh
308 = 2 × (22/7) × r × 14
⇒ 308 = 88r
⇒ r = 7/2 = 3.5 cm
Volume = πr2h
⇒ Volume = (22/7) × (3.5)2 × 14
⇒ Volume = 539 cm3
∴ Volume of the cylinder is 539 cm3
See lessA piece of tin is in the form of a ractangle having length 12 cm and width 8 cm. This is used to construct a closed cube. The side of the cube is:
1. 2 cm
2. 3 cm
3. 4 cm
4. 6 cm
Correct Answer - Option 3 : 4 cmGiven Length of rectangle = 12 cm Width of rectangle = 8 cm Formula used Area of rectangle = length × breadthTotal surface area of cube = 6(side)2Calculation ⇒ Area of rectangle = surface area of cube ⇒ 12 × 8 = 6 × side2⇒ side of cube = 4 cm ∴ the side of the cubeRead more
Correct Answer – Option 3 : 4 cm
Given
Length of rectangle = 12 cm
Width of rectangle = 8 cm
Formula used
Area of rectangle = length × breadth
Total surface area of cube = 6(side)2
Calculation
⇒ Area of rectangle = surface area of cube
⇒ 12 × 8 = 6 × side2
⇒ side of cube = 4 cm
∴ the side of the cube is 4 cm
See less3D bodies occupy a portion of the space. The extent of space occupied by a 3D body is its ______.
1. Time-measure
2. Volume-measure
3. Distance-measure
4. Weight-measure
Correct Answer - Option 2 : Volume-measureMeasurement: It is defined as the description of data in terms of numbers. More precisely, measurement is defined as the assignment of numerals to objects or events according to rules.3-dimensional body: A body that has length, breadth, and height. For examRead more
Correct Answer – Option 2 : Volume-measure
Measurement: It is defined as the description of data in terms of numbers. More precisely, measurement is defined as the assignment of numerals to objects or events according to rules.
3-dimensional body: A body that has length, breadth, and height. For example, glass, ball, and cylinder are three-dimensional objects as it has length, breadth, and height.
Hence, we conclude that the extent of space occupied by a 3D body is its volume measure.
See lessIf the altitude of an equilateral triangle is 4√3 cm, then find the area of an equilateral triangle.
1. 16√3
2. 8√3
3. 64√3
4. 24√3
Correct Answer - Option 1 : 16√3GivenThe altitude of an equilateral triangle = 4√3ConceptAltitude of an equilateral triangle = (√3/2) × sideArea of an equilateral triangle = (√3/4) × (side)2CalculationAccording to the question4√3 = (√3/2) × side⇒ Side = [(4√3) × 2]/√3⇒ Side = 8 cmNow, ⇒ Area of an eRead more
Correct Answer – Option 1 : 16√3
Given
The altitude of an equilateral triangle = 4√3
Concept
Altitude of an equilateral triangle = (√3/2) × side
Area of an equilateral triangle = (√3/4) × (side)2
Calculation
According to the question
4√3 = (√3/2) × side
⇒ Side = [(4√3) × 2]/√3
⇒ Side = 8 cm
Now,
⇒ Area of an equilateral triangle = (√3/4) × 82
⇒ Area of an equilateral triangle = 16√3 cm2
∴ Area of an equilateral triangle = 16√3 cm2
See less1 cm त्रिज्या वाले 2 बराबर सिक्के एक दूसरे को स्पर्श करते हुए मेंज पर रखें हैं सिक्कों द्वारा घिरा क्षेत्रफल ज्ञात करें?
A. `((pi)/2-sqrt(3) cm^(2)`
B. `(sqrt(3)-(pi)/2) cm^(2)`
C. `(2sqrt(3)-(pi)/2) cm^(2)`
D. ` (3sqrt(3)-(pi)/2)cm^(2)`
Correct Answer - Bप्रत्येक वृत्त की त्रिज्या `=1cm` With all three centres an equilateral triangle of side 2 cm is formed. सिक्कों द्वारा परिबद्ध क्षेत्रफल `=` (area of equilateral triangle) `3xx` (area of sector of angle `60^(@)`) `=(sqrt(3))/4(2)^(2)-3xx60/360xxpi(1)^(2)` `=(sqrt(3))/4xx4-3xx1/6xxRead more
Correct Answer – B
See lessप्रत्येक वृत्त की त्रिज्या `=1cm`
With all three centres an equilateral triangle of side 2 cm is formed.
सिक्कों द्वारा परिबद्ध क्षेत्रफल `=` (area of equilateral triangle) `3xx` (area of sector of angle `60^(@)`)
`=(sqrt(3))/4(2)^(2)-3xx60/360xxpi(1)^(2)`
`=(sqrt(3))/4xx4-3xx1/6xx pi`
`=(sqrt(3)-(pi)/2)cm^(2)`
If the radius of a sphere is 16 cm and is melted and recast into a sphere of radius 4 cm. Then find the number of small spheres that are cast.
1. 16
2. 32
3. 48
4. 64
Correct Answer - Option 4 : 64Given:Radius of an original sphere = 16 cmRadius of a recast sphere = 4 cmFormula Used:Volume of a sphere = (4/3)πr3 Number of recast spheres = Volume of the original sphere/Volume of the recast sphereCalculation:Volume of a original sphere = 4/3 π (16)3Volume of the rRead more
Correct Answer – Option 4 : 64
Given:
Radius of an original sphere = 16 cm
Radius of a recast sphere = 4 cm
Formula Used:
Volume of a sphere = (4/3)πr3
Number of recast spheres = Volume of the original sphere/Volume of the recast sphere
Calculation:
Volume of a original sphere = 4/3 π (16)3
Volume of the recast sphere = 4/3 π (4)3
Hence, number of recast spheres = Volume of the original sphere/Volume of the recast sphere
⇒ [(4/3) π (16)3]/[(4/3) π (4)3] = 64
∴ The number of recast spheres is 64.
See lessA circle of radius is equal to the diagonal of the square whose perimeter is numerically √3 times the area of an equilateral triangle with circumradius 4√3 cm. Find double the area of the circle with that radius.
1. 1458π cm2
2. 2916π cm2
3. 729π cm2
4. 2216π cm2
Correct Answer - Option 2 : 2916π cm2Given:Radius of circle = Diagonal of squarePerimeter of Square = √3 × area of equilateral triangle Circumradius of equilateral triangle = 4√3 cmFormulas Used:CircumRadius (R) = Side of equilateral triangle/√3Area of Equilateral Triangle = (√3/4) × (Side)2PerimetRead more
Correct Answer – Option 2 : 2916π cm2
Given:
Radius of circle = Diagonal of square
Perimeter of Square = √3 × area of equilateral triangle
Circumradius of equilateral triangle = 4√3 cm
Formulas Used:
CircumRadius (R) = Side of equilateral triangle/√3
Area of Equilateral Triangle = (√3/4) × (Side)2
Perimeter of Square = 4 × Side of square(a)
Diagonal of Square = √2 × Side of Square
Area of circle = π × (Radius)2
Calculation:
Side of equilateral triangle = √3 × 4√3 = 12 cm
Area of Equilateral Triangle = (√3/4) × (12)2 = 36√3 cm2
Here it is given that perimeter of square is √3 times the Area of equilateral triangle
Perimeter of Square = 4 × a = √3 × 36√3 = 108 cm
Side of Square (a) = 108/4 = 27 cm
Diagonal of Square = √2 × a = √2 × 27 = 27√2 cm
Radius of Circle (r) = Diagonal of square
⇒ r = 27√2 cm
Area of circle = π × (27√2)2 = 1458π
Double the area of circle = 2 × 1458π = 2916π
∴ Double the area of the circle is 2916π.
See lessThe area of an equilateral triangle is 36√3 m2. Find the perimeter of triangle.
1. 54 m
2. 45 m
3. 36 m
4. 48 m
Correct Answer - Option 3 : 36 mGiven :-Area of equilateral triangle = 36√3 m2Concept :-Area of an equilateral triangle = (√3/4) × Side2Perimeter of equilateral triangle = 3 × Side Calculation :-⇒ 36√3 = (√3/4) × Side2⇒ Side2 = 36 × 4⇒ Side = √(36 × 4)⇒ Side = 6 × 2 = 12 mNow,⇒ Perimeter of equilateRead more
Correct Answer – Option 3 : 36 m
Given :-
Area of equilateral triangle = 36√3 m2
Concept :-
Area of an equilateral triangle = (√3/4) × Side2
Perimeter of equilateral triangle = 3 × Side
Calculation :-
⇒ 36√3 = (√3/4) × Side2
⇒ Side2 = 36 × 4
⇒ Side = √(36 × 4)
⇒ Side = 6 × 2 = 12 m
Now,
⇒ Perimeter of equilateral triangle = 3 × 12
⇒ Perimeter of equilateral triangle = 36 m
∴ Perimeter of equilateral triangle is 36 m
See less