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Find the area and the circumference of a circle with diameter 5 yd. Use the value 3.14 for n, and do not round your answers. Be sure to include the correct units in your answers.

Question

Find the area and the circumference of a circle with diameter 5 yd. Use the value 3.14 for n, and do not round your answers. Be sure to include the correct units in your answers.

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Solution

To find the area and the circumference of a circle, we need to use the formulas:

Area = πr² Circumference = 2πr

where r is the radius of the circle and π is a constant approximately equal to 3.14.

Given that the diameter of the circle is 5 yards, the radius would be half of the diameter, which is 2.5 yards.

  1. Calculate the area: Substitute r = 2.5 yd into the formula for area: Area = π(2.5 yd)² = 3.14 * (2.5 yd)² = 3.14 * 6.25 yd² = 19.625 yd²

  2. Calculate the circumference: Substitute r = 2.5 yd into the formula for circumference: Circumference = 2π(2.5 yd) = 2 * 3.14 * 2.5 yd = 15.7 yd

So, the area of the circle is 19.625 square yards and the circumference is 15.7 yards.

This problem has been solved

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