A rectangular prism is shown below. What is the volume of the prism? A 12(3)/(256) cubic inches B 35(3)/(4) cubic inches C 48(3)/(64) cubic inches D 57(3)/(4) cubic inches

Question

A rectangular prism is shown below. What is the volume of the prism?

A
`12(3)/(256)` cubic inches

B
`35(3)/(4)` cubic inches

C
`48(3)/(64)` cubic inches

D
`57(3)/(4)` cubic inches

Answer 1

`\large\boxed{D.\ 57(3)/(8)\ in^3}`

Explanation:

Look at the picture.

The little cube has a volume 1/8 in³.

Calculate the number of small cubes, in the same way as we count the volume of a rectangular prism:

`V=lwh`

l - length (11)

w - width (6)

h - height (7)

Substitute:

`V=(11)(6)(7)=462`

The volume of the one small cubes is 1/8 in³.

Therefore the toatal volume is:

`V=462\left((1)/(8)\ in^3\rifgt)=(462)/(8)\ in^3=57(3)/(8)\ in^3`