Question

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ara Sutton - Cla..

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6 points

2. The seniors at our high school decided to play a prank on the principal

by completely filling his office with basketballs. To determine the number

of basketballs needed the students measured the room after moving out

the furniture. If the room measured 15 ft by 20 ft by 10 ft, approximately

how many basketballs did the students put in the principal's office? The

basketballs had a diameter of 9.2 inches. (Volume of sphere = (4/3)Nr3)

Answer 1

12709 balls

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 = (4)/(3)\pi r^3`

Where

`r = (1)/(2) * Diameter`

`r = (1)/(2) * 9.2`

`r = 4.6\ in`

So:

`Volume = (4)/(3)\ * (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 = (3000\ ft^3)/(407.88419\ in^3)`

Convert ft^3 to in^3

`Balls = (3000 * 1728in^3)/(407.88419\ in^3)`

`Balls = (3000 * 1728)/(407.88419)`

`Balls = (5184000)/(407.88419)`

`Balls = 12709.4899167`

`Balls = 12709` -- approximated

Hence, the room will contain 12709 balls