The sum of the circumference of a circle and the perimeter of a rectan...
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.