If the ratio of radius of two spheres is 4:7, the ratio of their volume is?

64 : 343

Step-by-step explanation:

First use the radii to find the volume

1) Radius of first sphere is 4 (taken from 4:7 ratio)

Insert it into the equation for volume of a sphere: V=4 / 3πr^3

V = (4/3) (π) (4^3)

V = (4/3) (π) (64)

V = 256/3 π

Volume of the first sphere = 256/3 π

2) Radius of the second sphere is 7 (also taken from 4:7 ratio)

Insert it into the equation for volume of a sphere: V=4 / 3πr^3

V = (4/3) (π) (7^3)

V = (4/3) (π) (343)

V = 1372/3 π

Volume of the second sphere = 1372/3 π

Next, calculate the ratio by dividing the two numbers

256/3 π : 1372/3 π

Answer should be 64 : 343

The simple way to do this problem is to just cube the numbers:

4:7 becomes 4^3 : 7^3 = 64 : 343

Either way works.