Questions: The radius of a circle is 9 m. Answer the parts below. Make sure that you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact circumference and area of the circle. Write your answers in terms of π. Exact circumference: 18 π m Exact area: 81 π m^2 (b) Approximate the circumference and area of the circle. To do the approximations, use the π button on the ALEKS calculator and round your answers to the nearest hundredth. Approximate circumference: Approximate area:

The radius of a circle is 9 m. Answer the parts below. Make sure that you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact circumference and area of the circle. Write your answers in terms of π. Exact circumference: 18 π m Exact area: 81 π m^2 (b) Approximate the circumference and area of the circle. To do the approximations, use the π button on the ALEKS calculator and round your answers to the nearest hundredth. Approximate circumference: Approximate area:
Transcript text: The radius of a circle is 9 m . Answer the parts below. Make sure that you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact circumference and area of the circle. Write your answers in terms of $\pi$. Exact circumference: $18 \pi \mathrm{~m}$ Exact area: $81 \pi \mathrm{~m}^{2}$ (b) Approximate the circumference and area of the circle. To do the approximations, use the $\pi$ button on the ALEKS calculator and round your answers to the nearest hundredth. Approximate circumference: $\square$ Approximate area: $\square$
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Solution

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Solution Steps

Step 1: Given the radius of the circle as 9, first find the radius (if necessary).
For a given radius, the radius is calculated as \(r = \frac{d}{2} = 9\) if the diameter is provided.
Step 2: Use the formula for the circumference of a circle \(C = 2\pi r\).
Substituting the given values, \(C = 2\pi \times 9\).

Final Answer: The exact circumference of the circle is \(2\pi \times 9\) in terms of \(\pi\).

Step 1: Given the radius of the circle as 9, first find the radius (if necessary).
For a given radius, the radius is calculated as \(r = \frac{d}{2} = 9\) if the diameter is provided.
Step 2: Use the formula for the area of a circle \(A = \pi r^2\).
Substituting the given values, \(A = \pi \times 9^2\).
Final Answer: The exact area of the circle is \(\pi \times 9^2\) or \(\pi \times 81\) in terms of \(\pi\).
Step 1: Given the radius of the circle as 9, first find the radius (if necessary).
For a given radius, the radius is calculated as \(r = \frac{d}{2} = 9\) if the diameter is provided.
Step 2: Use the formula for the circumference of a circle \(C = 2\pi r\).
Substituting the given values, \(C = 2\pi \times 9\).
Step 3: Calculate the approximate circumference using \(\pi pprox 3.142\).
Final Answer: The approximate circumference of the circle is 56.55.
Step 1: Given the radius of the circle as 9, first find the radius (if necessary).
For a given radius, the radius is calculated as \(r = \frac{d}{2} = 9\) if the diameter is provided.
Step 2: Use the formula for the area of a circle \(A = \pi r^2\).
Substituting the given values, \(A = \pi \times 9^2\).
Step 3: Calculate the approximate area using \(\pi pprox 3.142\).
Final Answer: The approximate area of the circle is 254.47.
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