Worksheet on Volume of Sphere

Perfect round balls contain measurable three-dimensional space inside. Mathematics explorers work with printable volume of sphere practice questions that reveal the elegant formula connecting radius to internal capacity. These captivating exercises help students understand how curved surfaces enclose space while applying calculations to sports balls, planets, and bubbles. Students can download the volume of sphere free PDF worksheet, each calculation builds spatial visualization and mathematical reasoning.

1. A spherical water tank has a diameter of 10 m. If the tank is filled to 80% of its capacity, what is the volume of the water in the tank? ( Use π = 3.14)

a) 418.66 m³
b) 523.33 m³
c) 420.44 m³
d) 318.18 m³

Answer: a)

Explanation: Given: diameter of the spherical tank, d= 10 m
Radius of the spherical tank, r = $\frac{\frac{d}{}}{\frac{2}{}}$ = $\frac{\frac{\mathrm{10}}{}}{\frac{2}{}}$ = 5 m
Volume of a spherical tank = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
                                            = $\frac{\frac{4}{}}{\frac{3}{}}$ x 3.14 x 5³
                                            = 523.33 m³

Since the tank is filled to 80% of its capacity
So, volume of the water in the tank = 80% of 523.33 = 418.66 m³

2. A sphere of radius 3 cm is melted and recast into smaller spheres each of radius 1 cm. How many smaller spheres can be made?

a) 9
b) 27
c) 81
d) 64

Answer: b)

Explanation: Let the radius of the original sphere be R and the radius of the smaller sphere be r.
Given that R = 3 cm and r = 1 cm
Volume of the original sphere = $\frac{\frac{4}{}}{\frac{3}{}}$πR³
                                                = $\frac{\frac{4}{}}{\frac{3}{}}$π(3)³ = 36π cm³

Volume of one smaller sphere = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
                                            = $\frac{\frac{4}{}}{\frac{3}{}}$π(1)³ = $\frac{\frac{4}{}}{\frac{3}{}}$π cm³
Number of smaller spheres = $\frac{\frac{\mathrm{Volume\; of\; the\; original\; sphere}}{}}{\frac{\mathrm{Volume\; of\; one\; smaller\; sphere}}{}}$
                                            = $\frac{\frac{\mathrm{36\pi }}{}}{\frac{\mathrm{4/3\pi }}{}}$ = 27

Hence, Total number of smaller spheres is 27.

3. An ice cream manufacturer produces ice cream in the shape of spheres with a diameter of 4 cm. If a customer buys an ice cream cone with 3 scoops, what is the total volume of ice cream the customer gets?

a) 16π cm³
b) 32π cm³
c) 64π cm³
d) 96π cm³

Answer: b)

Explanation: Given the diameter of the sphere,d = 4 cm
Radius of the sphere,r = $\frac{\frac{d}{}}{\frac{2}{}}$ = 2 cm
Volume of one scoop = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
                                   = $\frac{\frac{4}{}}{\frac{3}{}}$π(2)³
                                   = $\frac{\frac{\mathrm{32}}{}}{\frac{3}{}}$π cm³

Volume of 3 scoops = 3 x $\frac{\frac{\mathrm{32}}{}}{\frac{3}{}}$π
                                = 32π cm³

4. The volume of a sphere is doubled. By what factor does the radius of the sphere increase?

a) ³√2
b) 2
c) √2
d) 4

Answer: a)

Explanation: The volume V of a sphere is given by:
V = $\frac{\frac{4}{}}{\frac{3}{}}$πr³ ----- (1)
Let the original volume be V and the new volume be 2V.
Let the original radius be r and the new radius be r′.

Then, 2V = $\frac{\frac{4}{}}{\frac{3}{}}$π(r′)³
2($\frac{\frac{4}{}}{\frac{3}{}}$πr³ ) = $\frac{\frac{4}{}}{\frac{3}{}}$π(r′)³ (Using (1))
         2r³ = r′³
            r' = ³√2r

5. A snowball melts and its radius decreases from 6 cm to 3 cm. By what factor has the volume of the snowball decreased?

a) 2
b) 4
c) 6
d) 8

Answer: d)

Explanation: The volume V of a sphere is given by:
V = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
Initial Volume = $\frac{\frac{4}{}}{\frac{3}{}}$π(6)³ = 288π
Final Volume = $\frac{\frac{4}{}}{\frac{3}{}}$π(3)³ = 36π

The factor by which the volume has decreased:
Factor = $\frac{\frac{\mathrm{288\pi }}{}}{\frac{\mathrm{36\pi }}{}}$ = 8

6. A manufacturing company produces ball bearings with a diameter of 2 cm. If one batch contains 1000 ball bearings, what is the total volume of ball bearings in the batch?

a) 4186.7 cm³
b) 2093.33 cm³
c) 523.60 cm³
d) 2618.40 cm³

Answer: a)

Explanation: Diameter of ball bearing = 2 cm
Radius of ball bearing, r = $\frac{\frac{2}{}}{\frac{2}{}}$ = 1 cm
Volume of 1 ball bearing = $\frac{\frac{4}{}}{\frac{3}{}}$π(1)³ = 4.1867 cm³

Total volume of 1000 ball bearings = 1000 x 4.186 = 4186.7 cm³

7. A spherical balloon of radius 4 cm is inflated such that its radius increases to 6 cm. By what factor does the volume of the balloon increase?

a) 1.5
b) 2.25
c) 3.375
d) 4

Answer: c)

Explanation: Volume of the initial balloon = $\frac{\frac{4}{}}{\frac{3}{}}$π(4)³ = $\frac{\frac{\mathrm{256\pi }}{}}{\frac{3}{}}$
Volume of the inflated balloon = $\frac{\frac{4}{}}{\frac{3}{}}$π(6)³
                                                  = $\frac{\frac{\mathrm{864\pi }}{}}{\frac{3}{}}$
                                                  = 288π

Factor by which the volume increases = $\frac{\frac{\mathrm{288\pi }}{}}{\frac{\mathrm{256\pi /3}}{}}$
                                                             = 3.375

8. A spherical tank is used to store oil. If the tank's diameter is 12 m, how much oil can it hold if it is filled to 75% of its capacity?

a) 904.32 m³
b) 565.49 m³
c) 678.24 m³
d) 847.95 m³

Answer: c)

Explanation: Diameter of tank, d = 12 m
Radius of the tank, r = $\frac{\frac{\mathrm{12}}{}}{\frac{2}{}}$ = 6 m
Volume of the tank = $\frac{\frac{4}{}}{\frac{3}{}}$π(6)³
                             = 288π
                             = 904.32 m³

Since the tank is filled to 75% of its capacity,
Quantity of oil it can hold = 75% x 904.32 m³
                                          = 678.24 m³

9. If a spherical bubble has a radius that is halved, by what factor does its volume change?

a) $\frac{\frac{1}{}}{\frac{2}{}}$
b) $\frac{\frac{1}{}}{\frac{4}{}}$
c) $\frac{\frac{1}{}}{\frac{8}{}}$
d) $\frac{\frac{1}{}}{\frac{\mathrm{16}}{}}$

Answer: c)

Explanation: Let r be the original radius and r′ be the new radius.
r′ = $\frac{\frac{r}{}}{\frac{2}{}}$
Original volume of spherical bubble = $\frac{\frac{4}{}}{\frac{3}{}}$π r³
New volume of spherical bubble = $\frac{\frac{4}{}}{\frac{3}{}}$π (r')³
                                                     = $\frac{\frac{4}{}}{\frac{3}{}}$π ($\frac{\frac{r}{}}{\frac{2}{}}$)³
                                                     = $\frac{\frac{1}{}}{\frac{8}{}}$ ($\frac{\frac{4}{}}{\frac{3}{}}$π r³) = $\frac{\frac{V}{}}{\frac{8}{}}$

Thus, the volume changes by a factor of $\frac{\frac{1}{}}{\frac{8}{}}$.

10. A spherical balloon has a volume of 38808 m³. What is the radius of the balloon?

a) 22 m
b) 7 m
c) 21 m
d) 14 m

Answer: c)

Explanation: It is given that Volume of spherical balloon = 38808 m³
Using a formula for the volume of a sphere to find r
V = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
33808 = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
On solving, r = 21 m

Thus, the radius of the balloon is 21 m.