Question

Two beach balls are put inside a cylindrical container displayed in the image below. The cylinder has a radius of 6cm and height of 20 cm, the smaller beach ball has a diameter of 6cm and the larger beach ball has a diameter of 7cm. a) Find the amount of space that is unoccupied by the two beach balls in this container, to the nearest tenth of a cubic centimeter.

Answer 1

Answer:

1968.3cm^3

Step-by-step explanation:

The diagram for the question wasn't attached. We can still solve using the given parameters.

Solution:

Given:

Radius of cylinder= 6cm

Height of cylinder = 20cm

Diameter of smaller beach ball, d = 6cm

It's radius, r = d/2 = 6/2 = 3cm

Diameter of larger beach ball, D = 7cm

It's Radius, R = D/2 = 7/2 = 3.5cm

Amount of space that is unoccupied by the two beach balls in this container

= Volume of cylinder - Volume of both beach balls

Volume of cylinder (V) = πr^2h

V = π × (6×6×20)

V = 2260.8cm^3

Volume of smaller beach ball = volume of sphere = 4/3 × (πr^3)

Volume of smaller beach ball = (4/3)(π×3×3×3)

Volume of smaller beach ball = 113.04cm^3

Volume of larger beach ball = 4/3 × (πr^3)

Volume of larger beach ball = (4/3)(π×3.5×3.5×3.5)

Volume of larger beach ball = 179.50cm^3

Volume of both beach balls = Volume of smaller beach ball + Volume of larger beach ball

= 113.04cm^3 + 179.50cm^3

Volume of both beach balls = 292.54cm^3

Amount of space that is unoccupied by the two beach balls in this container = 2260.8cm^3 - 292.54cm^3

= 1968.26cm^3

Amount of space that is unoccupied by the two beach balls in this container = 1968.3cm^3 (nearest tenth)