The perimeter of a semicircle is 17.476 centimetres. What is the semicircle's diameter?
Question
The perimeter of a semicircle is 17.476 centimetres. What is the semicircle's diameter?
Solution
The perimeter of a semicircle is given by the formula P = πd + d, where P is the perimeter, d is the diameter, and π is approximately 3.14.
Given that the perimeter P is 17.476 cm, we can set up the equation:
17.476 = πd + d
To solve for d, we first combine like terms:
17.476 = d(π + 1)
Then, we divide both sides by (π + 1) to isolate d:
d = 17.476 / (π + 1)
Using a calculator, we find that:
d ≈ 17.476 / 4.14 ≈ 4.22 cm
So, the diameter of the semicircle is approximately 4.22 centimetres.
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