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

User Dethos
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1 Answer

2 votes

Answer:

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.

User Javi
by
7.9k points

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