Question

A path of 3.5 m width runs around a semi circular grassy plot whose perimeter is 72m .find area of path

Answer 1

Answer:

$\text{The area of path is }173.25 m^2$

Step-by-step explanation:

Given that a path of 3.5 m width runs around a semi circular grassy plot whose perimeter is 72 m. we have to find the area of path.

Let the radius of the semicircular grass plot be r.

Now, Perimeter of a semicircular grassy is Circumference of semicircular grassy plot + diameter of semicircular grassy plot

Perimeter=πr+2r

⇒ $72=(\frac{22}{7}+2)r$

⇒ $72=\frac{36}{7}r$

⇒ $72\times\frac{7}{36}=r$

⇒ r=14 m

Now, radius of path can be calculated as

R=14 + 3.5 = 17.5 m

Now, Area of path is given by

=$\frac{1}{2}\pi R^2-\frac{1}{2}\pi r^2$

=$\frac{1}{2}\pi (R^2-r^2)$

=$\frac{1}{2}\times \frac{22}{7}((17.5)^2-14^2)$

=$\frac{22}{14}(306.25-196)$

=$\frac{22}{14}\times 110.25=173.25 m^2$

Hence, $\text{the area of path is }173.25 m^2$