Question

pomodoro's has just created a deep dish pizza box since their old boxes are not tall enough. The new pizza has a radius of 8 inches and a height of 2 inches. to minimize the cost of the box and to preserve the quality of the pizza they want the box to be one inch taller than the pizza and an extra half inch on each side of the pizza.a) determine the dimensions of the boxb) determine the volume of the boxc) determine the volume of the pizza

Answer 1

a) 17 inches long; 17 inches wide; 3 inches tall.

b) 867 in³

c) 402.12 in³

Step-by-step explanation

a) This is a diagram of the pizza and the box:

The box must be 1 inch taller than the pizza, so if the pizza is 2 inches tall, then the box is 3 inches tall.

Then it says that they want half extra inch on each side of the pizza, so the distance from the center of the pizza to the side of the box should be 8.5 inches. The total width of the box is twice that distance: 17 inches. And since the pizza is a circle, the length of the box is the same size: 17 inches.

b) The box is a square prism. Its volume is the product of its dimensions:

`V=17in*17in*3in=867in^3`

c) The pizza is circular, so it is a cylinder. The volume is the area of the base multiplied by its height:

`V=\pi r^2h=\pi\cdot8^2\cdot2=\pi\cdot64\cdot2=128\pi\approx402.12in^(3)`