The perimeter of a semicircle is 25.7 kilometres. What is the semicircle's radius?
Question
The perimeter of a semicircle is 25.7 kilometres. What is the semicircle's radius?
Solution
The perimeter of a semicircle is given by the formula P = πr + 2r, where r is the radius of the semicircle.
Given that the perimeter P is 25.7 kilometres, we can set up the equation:
25.7 = πr + 2r
To solve for r, we first combine like terms:
25.7 = r(π + 2)
Then, we divide both sides by (π + 2) to isolate r:
r = 25.7 / (π + 2)
Using the approximation π ≈ 3.14, we find:
r ≈ 25.7 / (3.14 + 2) ≈ 25.7 / 5.14 ≈ 5 kilometres
So, the radius of the semicircle is approximately 5 kilometres.
Similar Questions
The perimeter of a semicircle is 17.476 centimetres. What is the semicircle's diameter?
The area of a semicircle is 39.25 square metres. What is the semicircle's diameter?
The radius of a semicircle is 19 miles. What is the semicircle's perimeter?Use 𝜋 ≈ 3.14 and round your answer to the nearest hundredth. miles
What is the circumference of a circle that has an area of 50.24 square centimeters?
The radius of a semicircle is 16 centimeters. What is the semicircle's diameter? centimeters
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.