Question

1. a sector has a central angle of 60° and radius 12 cm. find its area. round to nearest tenth
2. a pizza with diameter 16 inches is cut into 8 equal slices. what is the area of one slice? round to nearest square inch

Explanation:

Problem 8:

Step1: Recall sector area formula

The formula for the area of a sector is \( A = \frac{\theta}{360^\circ} \times \pi r^2 \), where \( \theta \) is the central angle and \( r \) is the radius.

Step2: Identify given values

Here, \( \theta = 60^\circ \) and \( r = 12 \) cm.

Step3: Substitute values into formula

\( A = \frac{60^\circ}{360^\circ} \times \pi \times (12)^2 \)
Simplify \( \frac{60}{360} = \frac{1}{6} \), and \( (12)^2 = 144 \). So, \( A = \frac{1}{6} \times \pi \times 144 \)

Step4: Calculate the area

\( \frac{1}{6} \times 144 = 24 \), so \( A = 24\pi \approx 24 \times 3.1416 \approx 75.4 \) (rounded to nearest tenth)

Step1: Find the radius of the pizza

The diameter is 16 inches, so the radius \( r = \frac{16}{2} = 8 \) inches.

Step2: Recall the area formula for a circle

The area of a circle is \( A = \pi r^2 \).

Step3: Calculate the area of the whole pizza

Substitute \( r = 8 \) into the formula: \( A = \pi \times (8)^2 = 64\pi \) square inches.

Step4: Find the area of one slice

The pizza is cut into 8 equal slices, so the area of one slice is \( \frac{64\pi}{8} = 8\pi \approx 8 \times 3.1416 \approx 25.1 \) (rounded to nearest square inch)

Answer:

The area of the sector is approximately \( 75.4 \) square centimeters.

Problem 9: