Question

Bodie purchases a rectangular prism ( a box ) to store his dog food in. The prism is LaTeX: \frac{7}{4}7 4 inches long, LaTeX: \frac{9}{4}9 4 inches wide, and 3 inches in height. Bodie's dog food are these cute little cubes that are each LaTeX: \frac{1}{4}1 4 inches long, wide, and high. If Bodie carefully stacks the dog food into the prism, how many little dog food cubes will fit in the prism?

Answer 1

84dog cubes

Explanation:

First we need to get the volume of the rectangular prism and the little cubes

Volume of the prism = base area × height

Volume f the prism = length × width × height

Given

Length = 7/4in

Width = 9/4in

Height = 3in

Volume of the prism = 7/4×9/4×3

Volume of the prism = 63/48

Volume of the prism= 21/16 in³

Volume of the cube = L³

L is the length of one side of the cube

Volume of the cube =(1/4)³

Volume of tje cube = 1/64in³

Number of dog food cubes that will fit in = 21/16÷1/64

= 21/16×64/1

= 21×4

= 84

Hence 84 dog cubes will fit in