tennis ball are packed in a cylindrical container that contain 3 balls in a near fit. what fraction of the container is not occupied by the balls.?
Answers
Given:
3 balls are fitted in a cylinder container.
To Find:
The fraction of the container that is not occupied by the balls.
Solution:
Define x:
Let the radius of the ball be r units
The radius of the cylinder will also be r units
Find the height of the cylinder:
Height = 3 x diameter of the ball
Height = 3 (2r)
height = 6r units
Find the volume of the 3 balls:
Volume of 1 ball = 4/3 πr³
Volume of 3 balls = 4πr³ units³
Find the volume of the cylinder:
Volume = πr²h
Volume = πr²(6r)
Volume = 6πr³ unit³
Find the volume that is not occupied by the balls:
Volume not occupied by the balls = 6πr³ - 4πr³
Volume not occupied by the balls = 2πr³ unit³
Find the fraction of the container not occupied by the balls:
Fraction = 2πr³ ÷ 6πr³
Fraction = 1/3
Answer: 1/3
Answer:
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