Question

A man runs in a circular path. He runs towards the center from the circumference and after reaching the center he suddenly changes his direction from his original path at 180 degrees to the original direction and stopped when he reached the circumference. Find the area and perimeter of the circle, given that, the man ran 8 meters in the above-described path? [4 MARKS]

Answer 1

Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark
Given that
Total distance travelled by the man = 8 m
The man reached toward the center from the circumference to center and back to the center from the circumference.
So, the total distance covered by him is equal to twice the radius of the circle.
Let 'r' be the radius of the circle.

So, 2r = 8, r = 4

We know that area of the cicle is given by, Area=$\pi \times (r{)}^2{m}^2$

Area of the given circle =$\pi \times (4{)}^2{m}^2$
= $\left(3.14\right)\times \left(16\right)m^2$
=$50.24m^2$
The perimeter of a circle= $2\times \pi \times r$
=$2\times \pi \times 4$
=25.14 m

So, the area of the given circle is $50.24m^2$, and the perimeter is 25.14 m.