List of top Mathematics Questions on Volume of a Sphere

In a sphere, the rate of change of volume is:

If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is:

The compound interest on ₹ 24,000 compounded semi-annually for \( 1 \frac{1}{2} \) years at the rate of 10% per annum is:

The rate of change of the volume of a sphere with respect to its surface area $ S $ is

The side of a cube is equal to the diameter of a sphere. If the side and radius increase at the same rate then the ratio of the increase of their surface area is

The radius of a spherical ball is increasing at the rate of 1 m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by:

The volume of a sphere of radius r is obtained by multiplying its surface area with :

Match List I with List II

List-I		List-II
(A)	Volume of cone	(I)	\(\frac{1}{3}\pi h(r_1^2+r_2^2+r_1r_2)\)
(B)	Volume of sphere	(II)	\(\frac{1}{3}\pi r^2h\)
(C)	Volume of Frustum	(III)	\(\pi r^2h\)
(D)	Volume of cylinder	(IV)	\(\frac{4}{3}\pi r^3\)

Choose the correct answer from the options given below:

The radius of the sphere is increased by 100% then the volume of the resultant sphere is increased by

If the radius of a sphere is '2r' then the volume will be

If the diameter of a sphere is 'd' then its volume is

If the diameter of a sphere is d, then its volume is

If the radius of a sphere is tripled, then its volume will become

The radius of the sphere is increased by 100%, the volume of the resulting sphere is increased by

The diameter of a sphere is equal to the height of the cone of equal volume. If r and R are the radii of cone and sphere respectively, then r² =

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?

Find the volume of a sphere whose radius is
(i) 7 cm 
(ii) 0.63 m

Find the amount of water displaced by a solid spherical ball of diameter.
(i) 28 cm 
(ii) 0.21 m

The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm³ ?

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold?

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank.

Find the volume of a sphere whose surface area is 154 cm².

A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹4989.60. If the cost of whitewashing is ₹20 per square meter, find the
(i) inside surface area of the dome,
(ii) volume of the air inside the dome

Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the 
(i) radius r' of the new sphere, 
(ii) ratio of S and S'