Question

A cylindrical canister contains 3 tennis balls. Its height is 7 inches, and its radius is 1.5 inches. The diameter of one tennis ball is 2.25 inches. How much of the canister’s volume is unoccupied by tennis balls? Use 3.14 for π, and round your answer to the nearest hundredths place.

Answer 1

Given:

A cylindrical canister contains 3 tennis balls. Its height is 7 inches, and its radius is 1.5 inches. The diameter of one tennis ball is 2.25 inches.

To find:

How much of the canister’s volume is unoccupied by tennis balls? Use 3.14 for π, and round your answer to the nearest hundredths place.

Solution:

The dimensions of the cylindrical canister:

Height, h = 7 inches

Radius, r = 1.5 inches

∴ The volume of the cylindrical canister is,

= Volume of a cylinder

= $\pi r^2 h$

= $3.14 \times 1.5^2 \times 7$

= $49.455 \:cubic \:inches$

The dimensions of each tennis ball:

Diameter, d = 2.25 inches

So, radius, r = $\frac{d}{2} = \frac{2.25}{2} = 1.125 \:inches$

∴ The volume of 1 spherical-shaped tennis ball is,

= $\frac{4}{3} \pi r^3$

= $\frac{4}{3} \times 3.14 \times 1.125^3$

= $5.961 \:cubic\: inches$

No. of the tennis ball in the canister = 3

∴ The volume of 3 spherical-shaped tennis ball = 3 × 5.961 = 17.883 inches³

Now,

The volume of the canister that remains unoccupied by the tennis balls is,

= [Volume of the canister] - [Volume of 3 tennis balls]

= 49.455 - 17.883

= 31.572 inches³

rounding off to the nearest hundredths place

= 31.57 cubic inches

Thus, 31.57 cubic inches of the canister’s volume is unoccupied by tennis balls.

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