Questions: Consider the following figure. Give both exact values and approximations to the nearest hundredth. (a) Find the circumference (in cm ) of the figure. exact cm approximation cm (b) Find the area (in cm^2 ) of the figure. exact cm^2 approximation cm^2

Consider the following figure. Give both exact values and approximations to the nearest hundredth. (a) Find the circumference (in cm ) of the figure. exact cm approximation cm (b) Find the area (in cm^2 ) of the figure. exact cm^2 approximation cm^2
Transcript text: Consider the following figure. Give both exact values and approximations to the nearest hundredth. (a) Find the circumference (in cm ) of the figure. exact $\square$ cm approximation $\square$ cm (b) Find the area (in $\mathrm{cm}^{2}$ ) of the figure. exact $\square$ $\mathrm{cm}^{2}$ approximation $\square$ $\mathrm{cm}^{2}$
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Solution

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Solution Steps

Step 1: Identify the given information

The radius of the circle is given as 8 cm.

Step 2: Calculate the exact circumference

The formula for the circumference of a circle is \( C = 2\pi r \). Substitute \( r = 8 \) cm: \[ C = 2\pi \times 8 = 16\pi \text{ cm} \]

Step 3: Calculate the approximate circumference

Use the approximation \( \pi \approx 3.14 \): \[ C \approx 16 \times 3.14 = 50.24 \text{ cm} \]

Step 4: Calculate the exact area

The formula for the area of a circle is \( A = \pi r^2 \). Substitute \( r = 8 \) cm: \[ A = \pi \times 8^2 = 64\pi \text{ cm}^2 \]

Step 5: Calculate the approximate area

Use the approximation \( \pi \approx 3.14 \): \[ A \approx 64 \times 3.14 = 200.96 \text{ cm}^2 \]

Final Answer

(a) Find the circumference (in cm) of the figure.

  • Exact: \( 16\pi \) cm
  • Approximation: 50.24 cm

(b) Find the area (in cm\(^2\)) of the figure.

  • Exact: \( 64\pi \) cm\(^2\)
  • Approximation: 200.96 cm\(^2\)
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