Question

A right rectangular prism is packed with cubes of side length 1 over 2 inches. If the prism is packed with 5 cubes along the length, 3 cubes along the width, and 6 cubes along with the height, what is the volume of the prism?

A.Fraction 3 and 3 over 4 cubic inches

B.7 cubic inches

C.Fraction 11 and 1 over 4 cubic inches

D.24 cubic inches

Answer 1

Answer: C.Fraction 11 and 1 over 4 cubic inches

Explanation:

The volume of a rectangular prism of length L, width W, and height H is given by:

V=LWH

The prism is packed with cubes of a side length of a=1/2 inch. The volume of each cube is:

`V_c=a^3=\left((1)/(2)\right)^3=(1)/(8)\ in^3`

The prism is packed with L=5, W=3, and H=6, thus the volume (in cubes) is:

V=5*3*6=90\ cubes

Since each cube has a volume of
`(1)/(8) in^3`:

`V=90\cdot(1)/(8)=(45)/(4)`

Expressing as a mixed fraction:

`V=(45)/(4)=(44+1)/(4)=11(1)/(4)`

Answer: C.Fraction 11 and 1 over 4 cubic inches