Question

A small beach ball has a radius of 8 inches. A larger beach ball has a volume that is twice the volume of the small ball. What is the best approximation for the radius of the large beach ball?

Answer 1

V=(4/3)pir^3
find smaller
V=(4/3)pi8^3
V=(4/3)pi512
V=(2048/3)pi

twice of that
Vbig=2*(2048/3)pi
Vbig=(4096/3)pi
find radius
(4096/3)pi=(4/3)pir^3
divide both sides by pi
(4096/3)=(4/3)r^3
times both sides by 3
4096=4r^3
divide both sides by 4
1024=r^3
cube root both sides
8∛2=r
aprox
10.0794


the answer you are looking for is 8∛2 or 10.0794in or something close to that