Question

a 20 inch (in diameter) pizza is cut into various sizes. what is the area of a piece that was cut with a central angle of $35^{\circ}$?
the area of the piece of pizza is approximately $\square$ square inches.
(round to two decimal places as needed.)

Explanation:

Step1: Find pizza radius

The diameter is 20 inches, so radius $r = \frac{20}{2} = 10$ inches.

Step2: Calculate full pizza area

Use circle area formula: $A_{full} = \pi r^2 = \pi (10)^2 = 100\pi$ square inches.

Step3: Find slice area ratio

The slice's central angle is $35^\circ$, so the ratio of the slice to the full pizza is $\frac{35}{360}$.

Step4: Compute slice area

Multiply full area by the ratio: $A_{slice} = 100\pi \times \frac{35}{360}$
Simplify: $A_{slice} = \frac{3500\pi}{360} \approx \frac{3500 \times 3.1416}{360}$

Answer:

30.54 square inches