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The area of a semicircle is 6.28 square metres. What is the semicircle's radius?

Question

The area of a semicircle is 6.28 square metres. What is the semicircle's radius?

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Solution

The area of a semicircle is given by the formula A = 1/2 * π * r², where A is the area and r is the radius.

Given that the area A is 6.28 square metres, we can set up the equation 6.28 = 1/2 * π * r².

To solve for r, we first multiply both sides of the equation by 2 to get rid of the 1/2 on the right side. This gives us 2 * 6.28 = π * r², or 12.56 = π * r².

Next, we divide both sides of the equation by π to isolate r². This gives us r² = 12.56 / π.

Finally, we take the square root of both sides to solve for r. This gives us r = sqrt(12.56 / π).

Using a calculator, we find that r ≈ 2 metres. So, the radius of the semicircle is approximately 2 metres.

This problem has been solved

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