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Complete Question
A cylinder is eight inches high with a radius of three inches.It contains a ball with a diameter of five inches. What volume is left unoccupied in the cylinder?
Answer:
160.74 cubic inches
Step-by-step explanation:
Step 1
Find the volume of cylinder
= πr²h
A cylinder is eight inches high with a radius of three inches.
Height = 8 inches
Radius = 3 inches
Volume of the cylinder = π × 3² × 8
= 226.19 cubic inches
Step 2
Find the volume of sphere
= 4/3 π r³
It contains a ball with a diameter of five inches.
Diameter = Radius /2 = 5/2 = 2.5 inches
Volume of the Sphere = 4/3 × π × 2.5³
= 65.45 cubic inches
Step 3
What volume is left unoccupied in the cylinder?
This is calculated as:
Volume of Cylinder - Volume of sphere
= 226.19 cubic inches - 65.45 cubic inches
= 160.74 cubic inches
Therefore, the volume is left unoccupied in the cylinder is 160.74 cubic inches
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