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A water tank is in the shape of a cuboid. The edges of the tank are in the ratio 7 ∶ 5 ∶ 3. The surface area of the tank is 142 m2, find how many liters of water the tank can hold?
1. 105 kL
2. 110 kL
3. 102 kL
4. 108 kL
Correct Answer - Option 1 : 105 kLGiven:Ratio of sides = 7 ∶ 5 ∶ 3Total surface area of the tank = 142 m2Formula used:Total surface area of the cuboid = 2(lb + bh + hl)Volume of cuboid = l × b × h1m3 = 1000 litersCalculation:Let the sides of the tank = 7x, 5x and 3x∵ TSA of the tank = 2(lb + bh + hlRead more
Correct Answer – Option 1 : 105 kL
Given:
Ratio of sides = 7 ∶ 5 ∶ 3
Total surface area of the tank = 142 m2
Formula used:
Total surface area of the cuboid = 2(lb + bh + hl)
Volume of cuboid = l × b × h
1m3 = 1000 liters
Calculation:
Let the sides of the tank = 7x, 5x and 3x
∵ TSA of the tank = 2(lb + bh + hl)
⇒ 142 = 2[(7x × 5x) + (5x × 3x) + (3x × 7x)]
⇒ 142 = 2(35x2 + 15x2 + 21x2)
⇒ 142 = 2(71x2)
⇒ 71 = 71x2
⇒ x = √1 = 1 ——(Ignore the negative value)
∴ Sides of the tank are;
7x = 7 × 1 = 7m
5x = 5 × 1 = 5m
3x = 3 × 1 = 3m
∴ Volume of the tank in m3 = (7 × 5 × 3) m3 = 105 m3
∵ 1 m3 = 1000 liters
∴ 105 m3 = (1000 × 105) = 105000 liters = 105 kiloliters
∴ Tank can hold 105 kiloliters of water.
See less1 सेमी. और 6 सेमी. त्रिज्या के दो ठोस धात्विक गोलकों को पिघलाने पर 1 सेमी. मोटाई का खोखला गोला बनता है । खोखले गोले की बाहरी त्रिज्या क्या होगी?
A. 8 सेमी.
B. 9 सेमी.
C. 6 सेमी.
D. 7 सेमी.
Correct Answer - Bप्रथम ठोस गोले की त्रिज्या `=R=6cm` द्वितीय ठोस गोले की त्रिज्या `=r=1cm` खोखले गोले की आंतरिक त्रिज्या `x` खोखले गोले की बाहरी त्रिज्या `x+q` So `4/3pi(R^(3)+r^(3))=4/3pi{(x+1)^(3)-x^(3)}` `216+1=x^(3)+1+3x(x+1)-x^(3)` `216=3x(x+1)` `72=x^(2)+x` `implies x^(2)+x-72=0` After solvinRead more
Correct Answer – B
See lessप्रथम ठोस गोले की त्रिज्या `=R=6cm`
द्वितीय ठोस गोले की त्रिज्या `=r=1cm`
खोखले गोले की आंतरिक त्रिज्या `x`
खोखले गोले की बाहरी त्रिज्या `x+q`
So `4/3pi(R^(3)+r^(3))=4/3pi{(x+1)^(3)-x^(3)}`
`216+1=x^(3)+1+3x(x+1)-x^(3)`
`216=3x(x+1)`
`72=x^(2)+x`
`implies x^(2)+x-72=0`
After solving
`x=8cm`
खोखले गोले की बाहरी त्रिज्या
`=x+1=8+1=9cm`
Take `pi=22/7`
एक वृत्त तथा आयत का परिमाप समान हैं। आयत की भुजाऐं 26 cm तथा 18 cm हैं। वृत्त का क्षेत्रफल ज्ञात करें?
A. `125cm^(2)`
B. `230 cm^(2)`
C. `550 cm^(2)`
D. `616 cm^(2)`
Correct Answer - DPerimeter of circle `=2pir` `=2(18+26)=88cm` `implies pir=44cm` `r=14cm` `:.` Area of circle `=22/7xx14xx14` `=616cm^(2)`
Correct Answer – D
See lessPerimeter of circle `=2pir`
`=2(18+26)=88cm`
`implies pir=44cm`
`r=14cm`
`:.` Area of circle `=22/7xx14xx14`
`=616cm^(2)`
A conical cap has the base radius 12 cm and height 16 cm. What is the cost of painting the surface of the cap at the rate of 1.40 Rs. per sq. cm?
1. Rs. 1276
2. Rs. 1056
3. Rs. 1012
4. Rs. 1254
Correct Answer - Option 2 : Rs. 1056Given: Radius of conical cap = 12 cmHeight of conical cap = 16 cmFormula used: Curved surface area of cone = πrll2 = r2 + h2 where, r = radius of conel = slant height of coneh = height of coneCalculation: l2 = 122 + 162 ⇒ l2 = 144 + 256 = 400⇒ l = √400 = 20 cmCurvRead more
Correct Answer – Option 2 : Rs. 1056
Given:
Radius of conical cap = 12 cm
Height of conical cap = 16 cm
Formula used:
Curved surface area of cone = πrl
l2 = r2 + h2
where, r = radius of cone
l = slant height of cone
h = height of cone
Calculation:
l2 = 122 + 162
⇒ l2 = 144 + 256 = 400
⇒ l = √400 = 20 cm
Curved surface area of cone = 22/7 × 12 × 20 = 5280/7 cm2
Cost of painting the surface of the cap = 5280/7 × 1.40 = 1056 Rs.
∴ The cost of painting the surface of the cap at the rate of 1.40 Rs per sq cm is Rs. 1056
See lessThe parallel sides of a trapezium are in the ratio 3 ∶ 5 and the perpendicular distance between them is 12 cm. The area of trapezium is 240 cm2. Find the length of the shorter side of the trapezium?
1. 21 cm
2. 12 cm
3. 18 cm
4. 15 cm
Correct Answer - Option 4 : 15 cmGiven:Ratio of Parallel sides = 3 ∶ 5Area of trapezium = 240 cm2Height of trapezium = 12 cmConcept:Replace the ratio with a constant and using the formula for the area of the trapezium, calculate the sides of the trapezium.Formula used:Area of trapezium = 1/2 × (SumRead more
Correct Answer – Option 4 : 15 cm
Given:
Ratio of Parallel sides = 3 ∶ 5
Area of trapezium = 240 cm2
Height of trapezium = 12 cm
Concept:
Replace the ratio with a constant and using the formula for the area of the trapezium, calculate the sides of the trapezium.
Formula used:
Area of trapezium = 1/2 × (Sum of parallel sides) × height
Calculation:
Let the parallel sides be 3x and 5x
Area of trapezium = 1/2 × (Sum of parallel sides) × height
⇒ 240 cm2 = 1/2 × (3x + 5x) × 12 cm
⇒ 240 cm2 = (1/2) × (8x) × 12 cm
⇒ 8x = (240 × 2)/12 cm
⇒ x = 40/8 cm
⇒ x = 5 cm
Shorter parallel side of the trapezium = 3x = 3 × 5 cm = 15 cm.
∴ Shorter parallel side of the trapezium is 15 cm.
See lessThe wire bent in the form of square encloses an area of 121 cm2. What is the enclosed area when same wire is bent in the form of circle?
1. 154 cm2
2. 150 cm2
3. 44 cm2
4. 77 cm2
Correct Answer - Option 1 : 154 cm2Given:Area of wire bent in the form of square = 121 cm2 Concepts used:Area of square = (Side)2The perimeter of wire bent in the form of square = Perimeter of wire bent in the form of the circleThe perimeter of square = 4 × side of the squarePerimeter/CircumferenceRead more
Correct Answer – Option 1 : 154 cm2
Given:
Area of wire bent in the form of square = 121 cm2
Concepts used:
Area of square = (Side)2
The perimeter of wire bent in the form of square = Perimeter of wire bent in the form of the circle
The perimeter of square = 4 × side of the square
Perimeter/Circumference of circle = 2πr
Area of circle = πr2
Where r → Radius
Calculation:
Area of square = (Side)2
⇒ 121 cm2 = (Side)2
⇒ Side = √121 cm
⇒ Side of square = 11 cm
The perimeter of wire bent in the form of square = 4 × side of the square
⇒ 4 × 11 cm
⇒ 44 cm
Let the radius of the circle be r cm.
Perimeter of wire bent in the form of square = Perimeter of wire bent in the form of circle
44 cm = 2πr
⇒ 44 cm = 2 × (22/7) × r
⇒ (44 × 7)/44 cm = r
⇒ r = 7 cm
Area of circle = πr2
⇒ 22/7 × (7)2 cm2
⇒ (22/7) × 49 cm2
⇒ 154 cm2
∴ The wire encloses an area of 154 cm2 when bent in the form of circle.
See lessएक आयताकार पानी की टंकी 80 मी `xx` 40 मी. है। इसमें 40 वर्ग सेमी. का पाईप, जो खोलने पर 10 किमी/घण्टा की गति से पानी भरता है। बताइए टंकी में आधे घण्टे में जल स्तर कितना ऊपर होगा?
A. `3//2 cm`
B. `4//9` cm
C. `5//9` cm
D. `5//8`cm
Correct Answer - DLet the water, `h` mtr. Will rise in the tank `lxxbxxh=` Area `xx` speed `xx` time `80xx40xxh=40/(100xx100)xx10000xx1/2` `h=1/160m=100/160cm=5/8cm`
Correct Answer – D
See lessLet the water, `h` mtr. Will rise in the tank
`lxxbxxh=` Area `xx` speed `xx` time
`80xx40xxh=40/(100xx100)xx10000xx1/2`
`h=1/160m=100/160cm=5/8cm`
If area of a square is 484 cm2. How long Its diagonal is:
1. 44 cm
2. 22√5 cm
3. 22 cm
4. 22√2 cm
Correct Answer - Option 4 : 22√2 cmGiven: Area of square = 484 cm2Formula Used:Area of square = side × sideDiagonal = √2 × sideCalculationArea of square = side × side⇒ √484 = side⇒ 22 cm = sideDiagonal = √2 × side⇒ Diagonal = √2 × 22⇒ Diagonal = 22√2 cm∴ The length of the diagonal is 22√2 cm.The corRead more
Correct Answer – Option 4 : 22√2 cm
Given:
Area of square = 484 cm2
Formula Used:
Area of square = side × side
Diagonal = √2 × side
Calculation
Area of square = side × side
⇒ √484 = side
⇒ 22 cm = side
Diagonal = √2 × side
⇒ Diagonal = √2 × 22
⇒ Diagonal = 22√2 cm
∴ The length of the diagonal is 22√2 cm.
The correct option is 4 i.e.22√2 cm.
See lessThe sum of all sides of triangle is 48 m and in radius is 7.5 m then find the area of triangle?
1. 180 square m
2. 210 square m
3. 220 square m
4. 240 square m
Correct Answer - Option 1 : 180 square mGiven:The sum of all sides of the triangle is 48 m and in radius is 7.5 mFormula used:Area of the triangle = (sum of all sides × r)/2Where r is the radius of the incircleCalculation:By using the given formula∴ Area = (48 × 7.5)/2 = 180 square mHence, option (1Read more
Correct Answer – Option 1 : 180 square m
Given:
The sum of all sides of the triangle is 48 m and in radius is 7.5 m
Formula used:
Area of the triangle = (sum of all sides × r)/2
Where r is the radius of the incircle
Calculation:
By using the given formula
∴ Area = (48 × 7.5)/2 = 180 square m
Hence, option (1) is correct
See lessA triangle and a parallelogram are constructed on the same base such that their area is the same. If the altitude of the parallelogram is 100 cm, then find the altitude of the triangle.
1. 200√2 cm
2. 220 cm
3. 200 cm
4. 240 cm
Correct Answer - Option 3 : 200 cmGIVEN:the altitude of the parallelogram = 100 cmFORMULA USED:Area of the parallelogram = (Base × Altitude) sq. unit and Area of triangle = (1/2 × Base × Altitude) sq. unitCALCULATION:Let the altitude of the triangle be L1 cm and the triangle and a parallelogram areRead more
Correct Answer – Option 3 : 200 cm
GIVEN:
the altitude of the parallelogram = 100 cm
FORMULA USED:
Area of the parallelogram = (Base × Altitude) sq. unit and Area of triangle = (1/2 × Base × Altitude) sq. unit
CALCULATION:
Let the altitude of the triangle be L1 cm and the triangle and a parallelogram are constructed on the same base
⇒ Area of the parallelogram = Area of triangle
⇒ (Base × Altitude) = (1/2 × Base × Altitude)
⇒ 100 = 1/2 × L1
⇒ L1 = 200 cm
∴ The altitude of the triangle is 200 cm
See less