Question

What is the difference in volume between a sphere with radius r and a sphere with radius 0.3r?

Answer 1

Answer:

$d = 1.2973\pi r^3$

Step-by-step explanation:

Given

$R_1 = r$

$R_2 = 0.3$

Required

The difference in their volumes

The volume of a sphere is:

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

So, the difference d is:

$d = \frac{4}{3}\pi [R_1^3 - R_2^3]$

$d = \frac{4}{3}\pi [r^3 - (0.3r)^3]$

$d = \frac{4}{3}\pi [r^3 - 0.027r^3]$

$d = \frac{4}{3}\pi *0.973r^3$

$d = \frac{3.892}{3}\pi r^3$

$d = 1.2973\pi r^3$