Question

The ratio of the volumes of two spheres is 827. What is the ratio of the lengths of the radi of these two spheres?

23

Answer 1

2/3

Explanation:

solve volume formula for r and then use v1 and v2 from the ratio to find r1 and r2

v = 4/3 Pi r**3

(3/4 v) / Pi = r**3

r = (3v/4Pi)**1/3

Then

r1 = (3*8/4pi)**3

= (6/Pi)**1/3

= 1.24

r2 = (3*27/4Pi)**3

= (81/4Pi)**3

= (6.45)**3

= 1.8

Then

r1/r2 = 1.24/1.8 = .6666666 or 2/3

Answer 2

2:3

Explanation:

r_1^3:r_2^3=8:27

r_1:r_2=2:3