Question

A rectangular piece of paper with length 30cm and width 12cm has two semicircles cut out of it. Find the area of the paper that remains. Use the value 3.14 for π, and do not round your answer.

Answer 1

88.5

Explanation

Assume R1 to be the radius of the first semi-circle and R2 be the radius of the second semi-circle.

Area of rectangle=A^2

=12 x 12 = 324

The remaining area

324 - 1/2*pi*R1^2 - 1/2*pi*r2^2 (where pi = 3.14)

= 324 -1/2*pi*(R1^2 + r2^2)

=324 - 1/2*pi*(10^2 + 5^2)

=324 - 1/2*pi*(100+50)

=324 - 1/2*pi*150

=324 - 0.5*3.14*150

=324 - 235.5

= 88.5