Question

jerome and jen are eating pizza. each pizza is sliced into 8 equal pieces. in your calculations below, use 3.14 for pi and round to the nearest hundredth. small pizza diameter: 10 inches large pizza diameter: 16 inches jerome eats two pieces of the small pizza. jeromes sector area eaten: select jen eats one piece of the large pizza. jens sector area eaten: (select) who ate more pizza? select

Explanation:

Jerome's Sector Area Eaten

Step1: Find radius of small pizza

The diameter of the small pizza is 10 inches, so the radius \( r = \frac{10}{2}=5 \) inches.

Step2: Find area of small pizza

The formula for the area of a circle is \( A=\pi r^{2} \). Using \( \pi = 3.14 \) and \( r = 5 \), we get \( A=3.14\times5^{2}=3.14\times25 = 78.5 \) square inches.

Step3: Find fraction of pizza Jerome ate

Each pizza is sliced into 8 equal pieces, and Jerome eats 2 pieces. So the fraction is \( \frac{2}{8}=\frac{1}{4} \).

Step4: Calculate Jerome's sector area

Multiply the area of the small pizza by the fraction: \( 78.5\times\frac{1}{4}=19.625\approx19.63 \) square inches.

Jen's Sector Area Eaten

Step1: Find radius of large pizza

The diameter of the large pizza is 16 inches, so the radius \( R=\frac{16}{2} = 8 \) inches.

Step2: Find area of large pizza

Using the area formula \( A=\pi R^{2} \) with \( \pi = 3.14 \) and \( R = 8 \), we get \( A=3.14\times8^{2}=3.14\times64=200.96 \) square inches.

Step3: Find fraction of pizza Jen ate

Jen eats 1 piece out of 8, so the fraction is \( \frac{1}{8} \).

Step4: Calculate Jen's sector area

Multiply the area of the large pizza by the fraction: \( 200.96\times\frac{1}{8}=25.12 \) square inches.

Who Ate More Pizza?

Compare Jerome's area (19.63) and Jen's area (25.12). Since \( 25.12>19.63 \), Jen ate more pizza.

Answer:

s:
Jerome's sector area eaten: \( \boldsymbol{19.63} \) square inches
Jen's sector area eaten: \( \boldsymbol{25.12} \) square inches
Who ate more pizza: \( \boldsymbol{Jen} \)