A baker is serving a new circular brownie pizza dessert (1" thick with a volume of 132.25 cubic inches). What are the dimensions of the open-topped cardboard box needed to serve the brownie pizza (assume the brownie to be inscribed in the box)?

1 Answer
Jan 6, 2018

Box measurement is **12.9764” x 12.9764” x 1”**

Explanation:

Volume of the pizza V_p = pi r^ h

Given

V_p = 132.25 cubic inch, h = 1”

132.25 = pi r^2 * 1

r^2 = 132.25 / (pi * 1) = 42.0965

r = sqrt (42.0965) = 6.4882”

Since pizza has a circular base, the bottom of the cardboard box will be a square with sides equal to the diameter of the pizza.

Let ‘a’ be the side of the square and ‘h’ the height equal to the thickness of pizza.

a = 2r = 2. 6.4882 = 12.9764”

h = 1”

Box measurement is **12.9764” x 12.9764” x 1”**