Question

It is given that the volume of a size 5 football is larger than that of a size 4 football by 72.8%.find the ratio of the radius of the size 5 football to that of the size 4 football.​

Answer 1

6/5

Explanation:

Let size 4 football radius = x,

and size 5 football radius = y,

Volume of size 5 = Volume of size 4 × (1 + 0.728)

Using the sphere volume formula,

V = (4/3)πr³

(4/3)πy³ = (4/3)πx³ × (1.728)

y³ = 1.728x³

y = ³√1.728 x

y/x = 6/5

Therefore, ratio of the radius of the size 5 football to that of the size 4 football is 6/5