Question

the diameter of the spherical football is four times of the diameter of the spherical tennis ball. find the ratio of their surface area​

Answer 1

Given :- The diameter of the spherical football is four times of the diameter of the spherical tennis ball.

To Find :-

• find the ratio of their surface area ?

Solution :-

Let us assume that, diameter of the spherical tennis ball is 2x cm.

So,

→ the diameter of the spherical football = 4 * diameter of the spherical tennis ball

→ the diameter of the spherical football = 4 * 2x = 8x cm.

Now,

→ radius of the spherical football = (Diameter/2) = 8x/2 = 4x cm.

→ radius of the spherical tennis ball = (Diameter/2) = 2x/2 = x cm.

Therefore,

→ Surface area of the spherical football = 4 * π * (radius)² = 4 * π * (4x)² = 4 * π * (16x²) = 64πx² cm².

→ Surface area of the spherical tennis ball = 4 * π * (radius)² = 4 * π * (x)² = = 4πx² cm².

Hence,

→ Surface area of the spherical football : Surface area of the spherical tennis ball = 64πx² : 4πx² = 16 : 1. (Ans.)

∴ Ratio of their surface area is 16 : 1.