Questions: The diameter of a circle is 16 ft. (a) Find the exact area of the circle. Write your answer in terms of pi. Exact area: (b) Using the ALEKS calculator, approximate the area of the circle. Approximate area:

The diameter of a circle is 16 ft. (a) Find the exact area of the circle. Write your answer in terms of pi. Exact area: (b) Using the ALEKS calculator, approximate the area of the circle. Approximate area:
Transcript text: The diameter of a circle is 16 ft. (a) Find the exact area of the circle. Write your answer in terms of $\pi$. Exact area: $\square$ (b) Using the ALEKS calculator, approximate the area of the circle. Approximate area: $\square$
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Solution

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Solution Steps

Step 1: Find the radius

The diameter of the circle is given as 16 ft. The radius is half the diameter, so the radius is 16 ft / 2 = 8 ft.

Step 2: Calculate the exact area

The area of a circle is given by the formula _A_ = _πr_², where _r_ is the radius. In this case, the radius is 8 ft, so the exact area is _A_ = _π_(8 ft)² = 64π ft².

Step 3: Calculate the approximate area

Using a calculator and the value of _π_, the approximate area is 64 * _π_ ≈ 201.06 ft². Rounding to the nearest hundredth gives 201.06 ft².

Final Answer

Exact area: 64π ft² Approximate area: 201.06 ft²

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