Question

A spherical balloon has an initial radius of 5 in. When more air is added, the radius becomes 10 in. How many times as great is the volume of the spherical with radius of 10 in as the spherical balloon with radius of 5 in?

Answer 1

To solve this problem, you must follow the steps below:

1. The formula for calculate the volume of a sphere, is:

V=4/3(πr³)

V is the volume of the sphere.
r is the radius of the sphere.

2. The initial volume of the spherical balloon with a radius of 5 inches, is:

V1=4/3(π)(5 in)³
V1=523.59 in³

3. The final volume of the spherical balloon with a radius of 10 inches, is:

V2=4/3(π)(10 in)³
V2=4188.79 in³

4. Then, you have:

V2/V1=4188.79 in³/523.59 in³=8

5. Therefore, the answer is:

The volume of the spherical balloon with a radius of 10 inches is 8 times greater than the spherical balloon with radius of 5 inches.

Answer 2

This question asking the ratio of 10inch ballon volume compared to 5 inch ballon volume. Since the ballon is sphere, you will need to use sphere volume.

V10/V5=
4/3 pi * 10^3 / 4/3 pi * 5^3 ----> remove 4/3 pi
10^3 / 5^3 ---> split 10 into 2*5
2^3 * 5^3 / 5^3 --->remove 5^3
2^3 /1= 8 times

10-inch ballon volume is 8 times greater than the 5-inch ballon volume