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)
