Q:

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

Accepted Solution

A:
Answer:64 : 343Step-by-step explanation:First use the radii to find the volume1) 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 π2) 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 πNext, calculate the ratio by dividing the two numbers256/3 π ÷ 1372/3 πAnswer should be 64 : 343The simple way to do this problem is to just cube the numbers:  4:7 becomes 4^3 : 7^3 = 64 : 343Either way works.