Volume of a Cylinder

Q.

A cylinder, a cone and a hemisphere all have an equal base and have the same height. The ratio of their volumes is

1. 3: 1: 2

2. 4: 5: 7

3. 3: 2: 1

4. 1: 2:3

Q. Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?

Q.

A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread evenly all around a width of 3 m it to form an embankment. Find the height of the embankment.

Q.

Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?

Q. Find the number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metallic cylinder of height 45 cm and diameter 4 cm.

Q.

The radii of the base of a cylinder and a cone are in the ratio 3 : 4. If they have their heights in the ratio 2 : 3, the ratio between their volumes is

(a) 9 : 8 (b) 3 : 4 (c) 8 : 9 (d) 4 : 3

Q. A hemispehrical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindircal bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.

Q.

Water flows at the rate of 15 km/hr through a pipe of diameter 14 cm into a cuboidal pond which is 50m long and 44m wide. In what time will the level of water in the pond rise by 21 cm?

Q.

A cylinder and a cone are of same base radius and of same height. The ratio of the volume of cylinder to that of the cone is:

1. 1:3

2. 2:3

3. 3:1

4. 1:2

Q.

The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respctively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.

Q.

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1

Q. Water is flowing at the rate of 2.52km/hr through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe

Q.

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 $c{m}^2$, find the volume of cylinder.

Q.

A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is 3m and its height is 3.5 m?

Q.

The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find:

(i) the volume

(ii) the total surface area.

Q.

150 spherical marbles, each of diameter 14 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.

Q.

The volume of a right circular cylinder with its height equal to the radius is $25\frac{1}{7}c{m}^3.$ Find the height of the cylinder.

Q.

From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed. Find the volume of the remaining solid.

Q.

In a hot water heating system, there is cylindrical pipe of length $28\mathrm{m}$and diameter $5\mathrm{cm}$. Find the total radiating surface in the system. (Assume$\mathrm{\pi }=\frac{22}{7}$)

Q.

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises by

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

Q.

The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 $m^2$.If the pipe is made of 99 $c{m}^3$ of metal, find the outer and inner radii of the pipe.

Q. A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of $\frac{3}{2}$ cm and its depth is $\frac{8}{9}$ cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape. [CBSE 2015]

Q.

Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80cm/ sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour ?

Q. Question 17
A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

Q.

Water running in a cylindrical pipe of inner diameter $7cm$, is collected in a container at the rate of $192.5$ litres per minute. Find the rate of flow of water in the pipe in $km/hr$.

Q.

A cylindrical road roller made of iron is 1m long.Its internal diameter is 54 cm and the thickness of the iron sheet used in making the roller is 9 cm.Find the mass of the roller, if 1 $c{m}^3$ of iron has 7.8 gm mass.$(Use\pi =3.14)$

Q. Question 14
Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm

Q.

A cylindrical pipe has an inner diameter of 7 cm and water flows through it at 192.5 litres per minute. Find the rate of flow.

1. 1

2. 3

3. 5

4. 6

Q.

Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm ?

Q.

The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq metres, find its volume.