Question

A 12-in. by 24-in. rectangular pizza is the same price as a pizza with a 10-in. diameter. Which shape will give you more pizza?

Answer 1

Answer:

Rectangular pizza.

Step-by-step explanation:

Let the price of the pizza be X, calculate the areas of the different pizzas to find which one has the largest area.

#Find the area of the rectangular pizza:

$A=lw, l=24\ in, \ w=12 \ in\\\\=24\times 12\\\\=288 in^2$

#Find the area of the circular pizza, given diameter is 10 in:

$A=\pi r^2=\pi(D/2)^2, \ D=10 \ in\\\\=\pi (10/2)^2\\\\=78.54 \ in^2$

#From our calculations, the rectangular pizza  is 3.7x the size of the circular pizza for the same amount.

$P_r=x\\P_c=x\\\\A_r>A_c\\\\288 \ in^2>78.54\ in^2$

Hence, the rectangular pizza will give you more pizza.