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A $3$ -inch-tall rectangular box with a square base is constructed to hold a circular pie that has a diameter of $8$ inches. Both are shown below. What is the volume, in cubic inches, of the smallest such box that can hold this pie? $\newline$ A. $24$ $\newline$ B. $64$ $\newline$ C. $72$ $\newline$ D. $192$ $\newline$ E. $512$

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GCF and LCM: word problems

Full solution

Q. A

3

-inch-tall rectangular box with a square base is constructed to hold a circular pie that has a diameter of

8

inches. Both are shown below. What is the volume, in cubic inches, of the smallest such box that can hold this pie?

\newline

A.

24

\newline

B.

64

\newline

C.

72

\newline

D.

192

\newline

E.

512

Determine dimensions of base: Determine the dimensions of the square base of the box. Since the pie has a diameter of $8$ inches, the square base must have sides of at least $8$ inches to accommodate the pie.
Calculate base area: Calculate the area of the square base. $\newline$ Area of a square = side length $\times$ side length $\newline$ Area = $8$ inches $\times$ $8$ inches = $64$ square inches
Calculate box volume: Calculate the volume of the box. $\newline$ Volume of a rectangular box = base area $\times$ height $\newline$ The height of the box is given as $3$ inches. $\newline$ Volume = $64$ square inches $\times$ $3$ inches = $192$ cubic inches
Match to answer choices: Match the calculated volume to the answer choices. $\newline$ The calculated volume is $192$ cubic inches, which corresponds to answer choice $D$ .

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