Question

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Answer 1

Answer:

12709 balls

Step-by-step explanation:

Given

Dimension of Room = 15 ft by 20 ft by 10 ft

Diameter of Ball = 9.2 inches

Required

Determine the number of balls that can be occupied by the room

First, we need to calculate the volume of the room

This is done by multiplying the dimensions of the room

$Volume = 15ft * 20ft * 10ft$

$Volume = 3000ft^3$

Next, we calculate the volume of the ball.

The ball is a sphere.

So:

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

Where

$r = \frac{1}{2} * Diameter$

$r = \frac{1}{2} * 9.2$

$r = 4.6\ in$

So:

$Volume = \frac{4}{3}\ * \frac{22}{7} * (4.6in)^3$

$Volume = 407.88419\ in^3$

To calculate the number of balls, we then divide the volume of the room by volume of a ball

$Balls = \frac{3000\ ft^3}{407.88419\ in^3}$

Convert ft^3 to in^3

$Balls = \frac{3000 * 1728in^3}{407.88419\ in^3}$

$Balls = \frac{3000 * 1728}{407.88419}$

$Balls = \frac{5184000}{407.88419}$

$Balls = 12709.4899167$

$Balls = 12709$ -- approximated

Hence, the room will contain 12709 balls