A truck is being filled with cube-shaped packages that have side lengths of \frac{1}{4} 4 1 ​ foot. The part of the truck that is being filled is in the shape of a rectangular prism with dimensions 8ft\times6\frac{1}{4}ft\times7\frac {1}{2}ft8ft×6 4 1 ​ ft×7 2 1 ​ ft.

Complete Question

A truck is being filled with cube-shaped packages that have side lengths 1/4 ​ foot. The part of the truck that is being filled is in the shape of a rectangular prism with dimensions 8ft × 6 1/4 ft × 7 1/2 ft. Find the number of cubes that can fill that part of the truck

1500 cubes

Step-by-step explanation:

Step 1

Find the volume of the cube

V = side length ³

V = (1/4 ft)³

V = 1/64

Step 2

Find the volume of the rectangular prism

= Length × Width × Height

= 8ft × 6 1/4 ft × 7 1/2 ft

= 8 × 25/4 × 15/2

= 375 ft³

Step 3

Number of cubes in the truck

Volume of the Rectangular Prism ÷ Volume of the cube

= 375ft³ ÷ 1/4ft³

= 375 × 4

= 1500 cubes

Therefore, the number of cubes that can fill that part of the truck(Rectangular prism) = 1500 cubes