Volume of a Cylinder

Q. Question 6
A milk tank is in the form of a cylinder whose radius is 1.5 m and length is 7 m. Find the Quantity of milk in liters that can be stored in the tank.

Q. Question 2
The diameter of cylinder A is 7 cm and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area.

Q.

In a cylinder, radius is doubled and height is halved, curved surface area will be

1. halved

2. doubled

3. same

4. four times

Q.

The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3.$The ratio of their volumes will be

(a) $4:9$

(b) $9:4$

(c) $20:27$

(d) $27:20$

Q.

The circumference of the base of a cylinder is 88 cm and its height is 60 cm. Find the volume of the cylinder and its curved surface area.

Q. The diameter and height of a cylindrical tank is 1.75 m and 3.2 m respectively. How much is the capacity of tank in litre? (π = $\frac{22}{7}$)

Q.

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

Q.

$66c{m}^3$ of silver is drawn into a wire $1mm$ in diameter. The length of the wire will be

(a) $78m$

(b) $84m$

(c) $96m$

(d) $108m$

Q.

$2.2cubicdm$ of brass is to be drawn into a cylindrical wire $0.25cm$ in diameter. Find the length of the wire.

Q.

The curved surface area of a cylinder is $4400c{m}^2$ and the circumference of its base is 110 cm. Find the volume of the cylinder.

Q.

A cylinder is open at both ends and is made of 1.5 cm thick metal. Its external diameter is 12 cm and height is 84 cm. What is the volume of metal used in making the cylinder? Also, find the weight of the cylinder if 1 cm 3 of the metal weighs 7.5 g.

Q.

A rectangular vessel 22 cm by 16 cm by 14 cm is full of water. If the total water is poured into an empty cylindrical vessel of radius 8 cm, find the height of water In the cylindrical vessel.

Q.

The height of a cylinder is 14 cm and its curved surface area is 264 $c{m}^2$.The volume of the cylinder is

(a) $308c{m}^3$

(b) $396c{m}^3$

(c) $1232c{m}^3$

(d) $1848c{m}^3$

Q.

Question 114

Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm, find its curved surface area.

Q.

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.

Q.

A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm. It is drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained?

Q.

The volume of a circular iron rod of length $1m$ is $3850c{m}^3$. Find its diameter.

Q.

The height of a cylinder is 14 cm and its diameter is 10 cm.The volume of the cylinder is

(a) $1100c{m}^3$

(b) $3300c{m}^3$

(c) $3500c{m}^3$

(d) $7700c{m}^3$

Q.

The volume of metal in a metallic cylinder pipe is $748c{m}^3$ , its length is $14cm$ and its external radius is $9cm$. Find its thickness.

Q.

A well is dug $20m$ deep and it has a diameter of $7m$. The earth which is so dug out is spread out on a rectangular plot $22m$ long and $14m$ broad, what is the height of the platform so formed?

Q.

A hollow garden roller of $42cm$ diameter and length $152cm$ is made of cast iron $2cm$ thick. Find the volume of iron used in the roller.

Q.

Question 91

The thickness of a hollow metallic cylinder is 2 cm. It is 70 cm long with outer radius of 14 cm. Find the volume of the metal used in making the cylinder, assuming that it is open at both the ends. Also, find its weight if the metal weighs 8 g per $c{m}^3$.

Q.

The radius and height of a cylinder are in the ratio $5:7$ and it's volume is $550c{m}^3.$ Find its radius.

Q.

A housing society consisting of $5500$ people needs $100L$ of water per person per day. The cylindrical supply tank is $7m$ high and has a diameter $10m$. For how many days will the water in the tank last for the society?

Q.

The length of a metallic tube is 1 metre, its thickness is 1 cm and its inner diameter Is 12 cm. Find the weight of the tube if the density of the metal is 7.7 grams per cubic centimetre.

Q.

How many litres of water flow out of a pipe in 1 minute if the area of cross section is 5 sq. cm and the speed of water in the pipe is 30 cm/s.

1. 6 litres

2. 10 litres

3. 15 litres

4. 9 litres

Q.

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per second into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes.

Q. Find the volume of a cylinder whose radius r is equal to its height.

1. $\pi r^2$
2. $\pi$
3. $\pi r$
4. $\pi r^3$

Q.

A particular brand of talcum powder is available in two packs, a plastic can with a square base of side $5cm$ and of height $14cm,$ or one with a circular base of radius $3.5cm$ and of height $12cm.$ Which of them has greater capacity and by how much?

Q.

The lateral surface area of a cylinder of length 14 m is $220m^2$. Find the volume of the cylinder.