What is the ratio of surface area to volume for a sphere? 

Solution:

We will use the concept of mensuration in order to find the ratio.

We know that volume and surface of a sphere if its radius is r is given by,

Volume of sphere = (4 / 3) π r³ 

Surface area of sphere = 4 π r²

We have to find the value of A / V.

Hence, A / V = (4 π r²) ÷ (4 / 3) π r³  = 3 / r

Hence, for a sphere of radius r, the ratio of surface area to volume is 3 / r.

What is the ratio of surface area to volume for a sphere? 

Summary:

For a sphere with radius r, the ratio of surface area to volume is 3 / r.