Volume of a Right Circular Cylinder

Q. The curved surface area of a cylindrical pillar is 264 sq. m and its volume is 924 cub. m. Find the ratio of its diameter to its height.

1. 7 : 6
2. 3 : 7
3. 7 : 3
4. 6 : 7

Q. Volume of a right circular cylinder of radius 2 cm and height 7 cm = cm${}^3$.

1. 88
2. 48
3. 168
4. 22

Q. A spherical shell of lead whose external radius is 9 cm is melted and recast into a right circular cylinder 8 cm high and 12 cm in diameter. Find the diameter of the shell. [4 MARKS]

Q. A rectangular box of metal $12$ cm x $15$ cm rolled along its length and a cylinder is formed. Find the volume of the cylinder. (Use $\pi =\frac{22}{7}$).

1. $150.18c{m}^3$
2. $180.18c{m}^3$
3. $170.18c{m}^3$
4. $160.18c{m}^3$

Q. Question 1
A copper wire, 3 mm in diameter is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per $c{m}^3$.

Q.

A tank of cylindrical shape has a radius of $2.8m$ and its height of $3.5m$. Complete the activity to find how many litres of water the tank will contain.

Q.

A cylindrical jar of height 'H' and radius 'R' is used to fill water in a cone of same height and radius. How many conical jars can it fill?

1. 9

2. 3

3. 6

4. 2

Q. A cylindrical cistern whose radius is 7 cm is partly filled with water. If a conical block of iron whose radius of the base is 3.5 cm and height is 6 cm is wholly immersed in the water, by how much will the water level rise? $(Use\pi =\frac{22}{7})$ [4 MARKS]

Q.

Juice is filled upto a height of 64 cm in a cylindrical container of radius 30 cm. It is served in small cylindrical cups of radius 6 cm and height 16 cm. If each cup is sold at ₹ 3, how much money can be earned by selling the juice?

1. ₹ 600

2. ₹ 100

3. ₹ 900

4. ₹ 300

Q.

Pavan filled water in a cylindrical vessel of radius $7cm$ and height $14cm.$ Then he gently dropped a spherical ball of radius $0.7cm.$ By how much should the height be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give the answer in micrometers and correct up to two decimal places.

___ $\mu m$

Q. Question 8
Two solid cones A and B are placed in a cylindrical tube as shown in the Fig.12.9. The ratio of their capacities are 2:1. Find the heights and capacities of cones. Also, find the volume of the remaining portion of the cylinder.

Q. If R is the outer radius of a hollow cylinder, r its inner radius, and h its height, then its volume (in cu. units) is:

1. $\pi (R-r{)}^{2}h$
2. $2\pi (R-r{)}^{2}h$
3. $\pi (R^2-r^2)h$
4. $2\pi (R^2-r^2)h$

Q.

If the radius of a cylinder is reduced by $50\%$, then volume of the cylinder will get reduced by

1. 25%

2. 50%

3. 75%

4. 40%

Q.

A tank is in the shape of a right circular cylinder whose radius and height are 7 cm and 14 cm respectively. The capacity of the tank is ___ $\times {10}^{-4}{m}^3$.

Q. A metallic cubiod of dimension $22cm.\times 15cm\times 7.5cm,$ was melted and cast into a cylinder of height $14cm.$ What is its radius?

Q.

A wheat hut is in the form of a cone has a radius of 3m and height of 14m. Find the capacity of the hut to store the wheat. [2 MARKS]

Q. If the radius of a cylinder is reduced by 50%, then find the percentage by which volume of the cylinder will be reduced.

1. 75

Q.

Water flows out through a circular pipe whose internal diameter is $2\mathrm{cm}$ at the rate of $6\mathrm{metre}\mathrm{per}\mathrm{second}$ into a cylindrical tank the radius of whose base is $60\mathrm{cm}$. How much will the level of water rise in $30\mathrm{minutes}$?

Q.

Water is stored up to its brim in a right circular cylinder whose volume is $100c{m}^3$. How many bottles of $10c{m}^3$ are required to empty the cylinder?

1. 10

2. 1

3. 0.1

4. 100

Q. The volume of material required to construct 7 cylindrical pillars having a circular base of radius 40 cm and of height 20 m = m${}^3$.

1. 7040
2. 70.4
3. 704
4. 7.04

Q.

A cylinder is having a volume of 231 cu. cm. If the height of the cylinder is 6 cm, then what is the radius of a ball which will fit inside the cylinder?

1. Circle

2. 4 cm

3. 2.5 cm

4. 5 cm

Q. A conical flask of base radius r and height h is full of milk. The milk is now poured into a cylindrical flask of radius $2r$. What is the height to which the milk will rise in the flask?

1. $\frac{h}{9}$
2. $\frac{h}{6}$
3. $\frac{h}{3}$
4. $\frac{h}{12}$

Q.

Theinner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm.The length of the pipe is 35 cm. Find the mass of the pipe, if $1c{m}^3$ of wood has a mass of 0.6 g. $[Assume\pi =\frac{22}{7}]$

1. 9.432 kg

2. 4.432 kg

3. 7.432 kg

4. 3.432 kg

Q.

Pavan completely filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 0.7 cm. By how much should the height of glass be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give the answer in micrometres and correct up to 2 decimal places. $1m={10}^{-6}\mu m$

1. 9333.33$\mu m$

2. 9666.67$\mu m$

3. 6666.67$\mu m$

4. 6333.33$\mu m$

Q.

The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height $10\frac{2}{3}cm$. Then, the diameter of the base of the cylinder = 7 cm.

1. True

2. False

Q. The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is:

1. 4:9
2. 9:4
3. 20:27
4. 27:20

Q.

A juice seller sells juice from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹ 10 for each cylindrical glass of juice whose height is 10 cm and radius is 4 cm. Find the total amount of money he earns by selling the juice.(Take $\pi =\frac{22}{7}$)

1. ₹ 220

2. ₹ 110

3. ₹ 170

4. ₹ 190

Q.

A cylinder has a volume of 231 $c{m}^3$. If the height of the cylinder is 6 cm, a ball can fit into the cylinder if it's radius is = ___.

1. Circle

2. 4 cm
3. 2.5 cm
4. 5 cm

Q.

Pavan filled water in a cylindrical vessel of radius 7cm and height 14cm. Then he gently dropped a spherical ball of radius 0.7cm. By how much should the height be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give the answer in micrometres and correct up to 2 decimal places ___ .

Q.

Pavan filled water in a cylindrical vessel of radius 7cm and height 14cm. Then he dropped a spherical ball of radius 0.7cm. Height should be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give answer in micrometre and correct up to 2 decimal places.