Lateral Surface Area of Cylinder

Q.

A cylindrical tank has a capacity of 6160 $m^3$. Find its depth if its radius is 14 m. Calculate the cost of painting its curved surface (outer) at the rate of Rs. 3 per $m^2$.

1. Rs. 3000

2. Rs. 2650

3. Rs. 2640

4. Rs. 2610

Q.

What is the volume of the trapezoidal prism?

Q.

A traditional “square” bale of hay is actually in the shape of a rectangular prism. Its dimensions are $2$ feet by $2$ feet by $4$ feet. How many square bales contain the same amount of hay as one large “round” bale?

Q.

The diameter of a road roller is 60 cm and it is 140 cm long. It levelled an area of $79,200c{m}^2$. How many turns did the road roller take to level the said area?

1. 4
2. 5
3. 3
4. 2

Q.

The inner diameter of a well is 2.5 m and it is 8 m deep. What would be the cost of cementing its inner wall at a rate of Rs. 350 per $m^2$ ?

1. Rs.20000

2. Rs.56000

3. Rs.27000

4. Rs.22000

Q. The diameter of a hollow pipe is 6 cm and it is 14 cm long. What would be the cost of cementing its outer surface if the cost of cementing is ₹ 100 per $c{m}^2$?

1. ₹ 28, 600
2. ₹ 26, 800
3. ₹ 24, 600
4. ₹ 26, 400

Q. The cost of painting the total outside surface of a closed cylinder at Rs$3perc{m}^2$ is Rs$2772$. If the height of the cylinder is $2$ times the radius, then find its volume.

Q.

A rectangular sheet of paper $40cm\times 44cm$ is rolled to form a hollow cylinder of height 40 cm. Find the diameter of the cylinder.

1. 7 cm

2. 10 cm

3. 14 cm

4. 15 cm

Q. The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in $m^2$?
$[Assume\pi =\frac{22}{7}]$

Q.

The diameter of a road roller is 44 cm and it is 1.4 m long.

What is the area of a levelled surface when it rolls once?

1. $1.178m^2$

2. $1.936m^2$

3. $1.777m^2$

4. $2.456m^2$

Q. What's the volume of the prism with a base of isosceles right-angled triangled in which two sides are of length 6 cm and one side of length $\sqrt{7}2$ cm and height of the prism is 10 cm?

1. $180c{m}^3$
2. $18c{m}^3$
3. $280c{m}^3$
4. $90c{m}^3$

Q. The base of a prism is a right triangle with the sides perpendicular to each other of lengths 5 cm and 10 cm, respectively. If the height of the prism is 100 cm, then find the amount of water it will displace when placed in a container filled with water.

Q. Match the unknown $x$ for a cylinder with radius 'r ', height '2r' and volume 'V' (all measures in cm).

1. 16π $c{m}^3$
2. 54π $c{m}^3$
3. 8 cm
4. 3 cm

Q.

There is a hollow jar of length 28 cm with lid removed from the top and bottom. The radius of this cylindrical hollow jar is 8 cm. If we have to cover the outer surface with paper, then the area of paper that is required will be equal to:

1. $1518{\text{cm}}^2$

2. $1408{\text{cm}}^2$

3. $1498{\text{cm}}^2$

4. $1428{\text{cm}}^2$

Q.

Raghu had to make a cylindrical aluminium tube. What is the area of the aluminium sheet required to make the tube if the length of the tube is $1m$ and base radius is $3.5cm?$ [Take $\pi =\frac{22}{7}$]

1. 2200 m²

2. 220 cm²

3. 220 m²

4. 2200 cm²

Q.

The inner diameter of a well is 2 m and it is 35 m deep. What would be the cost of cementing its inner wall at Rs. 500 per square meter ?

1. Rs. 1, 00, 000

2. Rs. 90, 000

3. Rs. 1, 10, 000

4. Rs. 1, 05, 000

Q.

YOU BE THE TEACHER Your friend finds the volume of the pyramid. Is your friend correct? Explain your reasoning.

Q.

A metallic prism of height 35 cm has a base as a right angled triangle. The triangle has a base length of 24cm and altitiude 10cm. It is melted and drawn into a cylindrical wire of radius 0.35 cm. What will be the length of wire drawn in metres?

1. 139.1 m

2. 209.1 m

3. 109.099 m

4. 91.11 m

Q. How much sheet (in $m^2$) is required to make an open cuboidal tank of L=5 m, B=10 m and H=3 m?

1. 140

Q. The thickness of a hollow wooden cylinder is $2cm$. It is $35m$ long and its inner radius is $12cm$. Find the volume of the wood required to make the cylinder, assuming it is open at either end.

1. $5720{cm}^3$
2. $322000{cm}^3$
3. $472000{cm}^3$
4. $502000{cm}^3$

Q.

A solid cylindrical party popper having radius 7 cm and length 20 cm needs to be gift wrapped by a paper sheet. What is the area of sheet required to cover it completely ?

1. $1198{\text{cm}}^2$

2. $1188{\text{cm}}^2$

3. $1248{\text{cm}}^2$

4. $1148{\text{cm}}^2$

Q. If the curved surface of a right circular cylinder is $1760c{m}^2$ and its radius is 21 cm, then its height is $\frac{80}{3}cm.$

1. True
2. False
3. Data insufficient
4. Ambiguous

Q. If the height and the slant height of a square pyramid are $8cm$ and $10cm$ respectively, what is the volume of the pyramid?

Q. If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true

1. Curved surface area will be 1 4 of the original curved surface.
2. curved surface area of the cylinder will remain unchanged.
3. Curved surface area of the cylinder will be doubled.
4. Curved surface area of the cylinder will be halved.

Q.

A log of wood is cylindrical in shape.The radius and height of the log is 1 cm and 6 cm respectively. What area needs to be covered if the log has to be painted completely ?

1. $48c{m}^2$

2. $44c{m}^2$

3. $52c{m}^2$

4. $54c{m}^2$

Q.

If the ratio of radii of two cylinders having the same height is 3 :4. The ratio of their curved surface area is

1. 3 : 4

2. 6 : 8

3. 9 :16

4. 16 : 25