Question

amal went to PetSmart to get his hamster an exercise ball. There was a small ball with a 6 inch diameter and a 12 inch one. The volume of the large ball halfeight timesfour timestwice

Answer 1

Answer:

The volume of the large ball is eight times the volume of the small ball

Explanation:

Given:

the diameter of the smaller ball = 6 inch

The diameter of the larger ball = 12 inch

To find

The volume of the larger ball in relation to the smaller one

A ball is spherical, we will be using the volume of a sphere:

$Volume\text{ of a sphere = }\frac{4}{3}\pi r^3$

For the smaller ball:

$\begin{gathered} diameter\text{ = 2\lparen radius\rparen} \\ radius\text{ = diameter/2 = 6/2 = 3 in} \\ \\ Volume\text{ of the smaller ball = }\frac{4}{3}\pi\times3^3 \end{gathered}$

For the larger ball:

$\begin{gathered} diameter\text{ = 12 in} \\ radius\text{ = 12/2 = 6} \\ \\ Volume\text{ of the larger = }\frac{4}{3}\pi\times6^3 \end{gathered}$$\begin{gathered} The\text{ ratio of larger ball to smaller ball = }\frac{\frac{4}{3}\pi\times6^3}{\frac{4}{3}\pi\times3^3}\text{ = 216/27} \\ \\ The\text{ ratio of larger ball to smaller ball = 8} \\ \\ \frac{volume\text{ of larger ball}}{volume\text{ of smaller ball}}=\text{ 8} \end{gathered}$

The volume of the large ball is eight times the volume of the small ball