# Mathematics Questions and Answers – Volume of a Sphere

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Volume of a Sphere”.

1. Volume of a sphere of radius r is equal to __________
a) $$\frac{4}{3} πr^3$$
b) πr2h
c) $$\frac{1}{3}$$ πr2h
d) $$\frac{2}{3} πr^3$$

Explanation: Volume of a sphere is $$\frac{4}{3}$$ π times the cube of a radius.
Therefore, volume of a sphere is equal to $$\frac{4}{3} πr^3$$.

2. Volume of a hemisphere of radius r is equal to __________
a) $$\frac{4}{3} πr^3$$
b) πr2h
c) $$\frac{1}{3}$$ πr2h
d) $$\frac{2}{3} πr^3$$

Explanation: Volume of a hemisphere is half the volume of a sphere.
We know that volume of a sphere of radius r is equal to $$\frac{4}{3} πr^3$$.
Therefore, volume of a hemisphere is equal to $$\frac{2}{3} πr^3$$.

3. What is the radius of a sphere having volume of 4851cm3? (Take π = $$\frac{22}{7}$$)
a) 9 cm
b) 11 cm
c) 10.5 cm
d) 11.3 cm

Explanation: We know that volume of a sphere of radius r is equal to $$\frac{4}{3} πr^3$$.
$$\frac{4}{3} πr^3$$ = 4851
$$\frac{4}{3} * \frac{22}{7} * r^3$$ = 4851
$$r^3 = \frac{9261}{8}$$
Therefore, r = $$\frac{21}{2}$$ = 10.5 cm.

4. Curved surface area of a hemisphere is equal to 2772 cm2, what is its volume? (Take π = $$\frac{22}{7}$$)
a) 19464 cm3
b) 19404 cm3
c) 19427 cm3
d) 19425 cm3

Explanation: We know that curved surface area of a hemisphere is equal to 2πr2.
2πr2 = 2772
r2 = $$\frac{2772*7}{2*22}$$ = 441
Therefore, r = 21cm
Now, we know that volume of a hemisphere is equal to $$\frac{2}{3}$$ πr3.
Hence, V = $$\frac{2}{3}$$ πr3
= $$\frac{2*22*21*21*21}{3*7}$$
= 19404 cm3.

5. A hollow sphere of outer radius of 4 cm and thickness of 3 cm is to be made from metal. What is the total amount of metal required (in cm3) to make the sphere? (Take π = $$\frac{22}{7}$$)
a) 281
b) 264
c) 225
d) 227

Explanation: Outer radius ro = 4cm
= 4 – 3
ri = 1cm
This means that the sphere is hollow and volume of metal required = $$\frac{4}{3} πr_o^3 – \frac{4}{3} πr_i^3$$
= $$\frac{4}{3} π (4^3 – 1^3)$$
= $$\frac{4*22*63}{3*7}$$
= 264 cm3.

6. Cost of whitewashing a sphere is 1232₹ at the rate of 2₹/cm2. What is the volume of a sphere? (Take π = $$\frac{22}{7}$$)
a) $$\frac{4324}{3}$$
b) $$\frac{4317}{5}$$
c) $$\frac{4312}{3}$$
d) $$\frac{4312}{7}$$

Explanation: Area of a sphere = $$\frac{Total \,cost \,of \,whitewashing}{Rate \,of \,whitewashing/cm^2}$$
= $$\frac{1232}{2}$$
= 616 cm2
We know that total surface area of a sphere = 4πr2
4πr2 = 616
r2 = $$\frac{616*7}{22*4}$$
= 49
Therefore, r = 7cm
Now, volume of a sphere = $$\frac{4}{3} πr^3$$
= $$\frac{4}{3} * \frac{22}{7}$$ * 73
= $$\frac{4312}{3}$$.

Sanfoundry Global Education & Learning Series – Mathematics – Class 9.