Question

A circular cloth with a diameter of 20 inches is placed on a circular tray with a diameter of 24 inches. What fraction of the tray's surface is not covered by the cloth?

Answer 1

the fraction of surface that is not covered is 11/36

Explanation:

To do this we first have to calculate the two surfaces

s = π * r^2

π = 3.14

r = d/2

d1 = 20

d2 = 24

r1 = 20/2

r1 = 10

r2 = 24/2

r2 = 12

s1 = π * r1^2

s1 = 3.14 * 10^2

s1 = 3.14 * 100

s1 = 314

s2 = π * r2^2

s2 = 3.14 * 12^2

s2 = 3.14 * 144

s2 = 452.16

to know the part that is not covered we simply do the s1 over the s2 and we subtract that from 1

s1 / s2 =

314 / 452.16 =

25/36

1 we subtract this

1 - 25/36 = 11/36

the fraction of surface that is not covered is 11/36