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.
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.
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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
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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.
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