Question

The perimeter of a semicircle is 34.438 inches. What is the semicircle's diameter?

Answer 1

diameter = 13.396 inches

Explanation:

The question asks us to calculate the diameter of a semicircle given that its perimeter is 34.438 inches.

To do this, we have to first think about the formula for the perimeter of a semicircle. Since a semicircle is made up of the diameter and half of the circumference of a regular circle, we can write the formula like this:

Perimeter = diameter + (
`\bf{(1)/(2)}` × circumference)

=
`2r + ((1)/(2) * 2 \pi r)`

=
`2r + \pi r`

=
`r (2 + \pi)`

We know the perimeter of the semicircle, and therefore, we can easily calculate its radius:

`34.438 = r (2 + \pi)`

⇒
`r = (34.438)/(2+ \pi)`

⇒
`r = \bf 6.698`

Next, we know that the diameter is twice the size of the radius, and therefore:

d = 2 × 6.698

= 13.396

Therefore, the diameter of the semicircle is 13.396 inches.