Answer:
64 : 343
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.