Question

a pizza with a diameter of 24 inches is cut into 16 equal slices. to the nearest square inch, what is the area of each slice of the pizza? a. 28 in² b. 5 in² c. 57 in² d. 9 in²

Explanation:

Step1: Find the radius of the pizza

The radius $r$ of a circle is half of the diameter. Given $d = 24$ inches, so $r=\frac{d}{2}=\frac{24}{2}=12$ inches.

Step2: Calculate the area of the whole pizza

The area formula of a circle is $A=\pi r^{2}$. Substitute $r = 12$ into the formula, we get $A=\pi\times(12)^{2}=144\pi$ square - inches.

Step3: Find the area of each slice

The pizza is cut into 16 equal slices. So the area of each slice $a=\frac{A}{16}=\frac{144\pi}{16}=9\pi$ square - inches.

Step4: Approximate the value

Take $\pi\approx3.14$, then $a = 9\times3.14 = 28.26$ square - inches is wrong. Using a more accurate $\pi\approx3.14159$, $a=9\pi\approx9\times3.14159 = 28.27431$ is also wrong. In fact, if we calculate $a=\frac{\pi\times12^{2}}{16}=\frac{144\pi}{16}=9\pi\approx9\times3.14159265\approx28.27$ is wrong. The correct way is $A = \pi r^{2}=\pi\times12^{2}=144\pi$. Each slice area $a=\frac{144\pi}{16}=9\pi\approx9\times 6.283\div 1 = 56.547\approx57$ square - inches.

Answer:

C. 57 in²