Question

Find the diameter of a semicircle with an area of 76.97 square yards

Answer 1

Circle Area = PI*r^2
Semi Circle Area = (PI*r^2)/2
76.97 = (PI*r^2)/2
76.97 * 2 / PI = radius^2
radius^2 = 76.97 * 2 / PI
radius^2 = 153.94 / PI
radius^2 = 49
radius = 7
Diameter = 14 yards

Answer 2

14 yards

Explanation:

The area of a semi circle is given by:

`A = (1)/(2) \pi r^2`

where, r is the radius of the semi-circle.

It is given that:

A = 76.97 sq. yards

`\Rightarrow (1)/(2) \pi r^2=76.97 \\ \Rightarrow r = \sqrt{(2* 76.97)/(\pi)} = 7 \text { yards}`

We know that diameter is twice of radius.

Thus, diameter of the semicircle is, d = 2 × 7 = 14 yards.