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)?

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Answer 1 · 2018-01-06T12:12:17

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

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”**#