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The sum of the circumference of a circle and the perimeter of a rectangle is 132 cm The area of the rectangle is 112 sq. cm and breadth of the rectangle is 8 cm. What is the area of the circle?
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Problem Statement

Find the area of the circle if the sum of the circumference of a circle and the perimeter of a rectangle is 132 cm where the area of the rectangle is 112 sq.cm and the breadth of the rectangle is 8 cm.


Solution

Let's start the solution by assuming the radius of the circle as r.


Step 1: Finding the perimeter of the rectangle

Given, breadth of the rectangle = 8 cm

Area of the rectangle = 112 sq.cm

Let's assume the length of the rectangle as l.

Then, Area of the rectangle = length x breadth

112 = l x 8

l = 14 cm

Perimeter of the rectangle = 2 x (length + breadth)

Perimeter of the rectangle = 2 x (14 + 8)

Perimeter of the rectangle = 2 x 22

Perimeter of the rectangle = 44 cm


Step 2: Finding the circumference of the circle

Formula to find the circumference of the circle is C = 2πr

where π is a constant with the value of approximately 3.14

Let's substitute the value of C and perimeter of the rectangle in the given equation

2πr + 44 = 132

2πr = 88

πr = 44

r = 14 cm


Step 3: Finding the area of the circle

Formula to find the area of the circle is A = πr^2

Let's substitute the value of r in the given equation

A = 3.14 x 14^2

A = 615.44 sq.cm


Answer

The area of the circle is 615.44 sq.cm.
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The sum of the circumference of a circle and the perimeter of a rectangle is 132 cm The area of the rectangle is 112 sq. cm and breadth of the rectangle is 8 cm. What is the area of the circle?
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