Volume of a Hollow Cylinder

Q. Find the volume of the iron used to make a hollow cylinder of height 9 cm and whose internal and external radii are 21 cm and 28 cm respectively.

1. $9720c{m}^3$
2. $9602c{m}^3$
3. $9700c{m}^3$
4. $9702c{m}^3$

Q.

A rectangle of length “a” and breadth “b” is revolved ${360}^{\circ }$ about its length. The volume of the resulting cylinder is

1. $\pi a{b}^2$

2. $\pi a^{2}b$

3. $\pi ab$

4. $2\pi ab$

Q. A solid cylinder of radius $\frac{R}{3}$ is removed from the solid cylinder of radius $R$ and length $L$. The volume of material in the hollow cylinder is $\frac{x}{9}\pi r^{2}L$.

1. 32

Q.

Question 3
How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic cm of iron weighs 7.5 g, find the weight of the box.

Q. A 7 m tube of inner diameter 8 cm and outer diameter of 4 cm is made of PVC used for electrical wiring. Find the space available for filling the copper wires inside it$(\pi \approx \frac{22}{7})$.

1. $0.0528m^3$
2. $0.0264m^3$
3. $0.0464m^3$
4. $0.0154m^3$

Q.

Q. The volume of a right circular cylinder with radius $6$ is $9\pi$. Calculate the height of the cylinder.

1. $\frac{1}{4}$ or $0.25$
2. $0.20$
3. $\frac{1}{3}$
4. $\frac{2}{5}$

Q. The volume of a cube = (side)${}^3$.

1. False
2. True

Q.

The ratio of surface areas of 1 cube of volume $64c{m}^3$ and 64 cubes of volume $1c{m}^3$ is:

1. 1 : 1

2. 1 : 3

3. 1 : 4

4. 1 : 2

Q. In a building there are $10$ cylindrical pillars . The radius of each pillar is $63$ cm and height is $15$ m. Find curved surface area of four pillars.

1. $22016m^2$
2. $2476m^2$
3. $237.6m^2$
4. None

Q. A fountain pen with a cylindrical barrel of diameter $3$ cm and height $14$ cm filled with ink can write $3600$ words. How many words can be written with that pen using $220$ ml of ink? (Take $1$ cc $=1$ ml)

1. $5000$
2. $6000$
3. $7000$
4. $8000$

Q. A cylinder perfectly fits into a cube as shown in the figure. If the side of the cube is a units that find the volume of the cylinder.

Q. A rectangle of length “$a$” and breadth “$b$” is rotated by ${360}^{\circ }$ about its length. The volume of the resulting cylinder is _____.

1. $\pi a{b}^2$
2. $\pi a^{2}b$
3. $\pi ab$
4. $2\pi ab$

Q. The volume of water required to fill half a tank of length 3 m, breadth 4 m and height 5 m is .

1. 30

Q.

The figure consists of 2 cylinders, the inner cylinder is a solid cylinder whose radius is r and the outer cylinder is a hollow cylinder whose radius is R and height is h, the volume of fluid it can hold is:

1. $\pi r^{2}h$

2. $\pi R^{2}h$

3. $\pi (R^2-r^2)h$

4. $\pi (R^2+r^2)h$

Q.

A hollow cylindrical pipe is 210 cm long. Its outer and inner diameters are 10 cm and 6 cm respectively. The volume of the copper used in making the pipe is

1. $10560{cm}^3$

2. $10570{cm}^3$

3. $10460{cm}^3$

4. $10260{cm}^3$