Question

The volume of a rectangular prism is 75 cubic inches. The height is 3 inches.

Which dimensions could be the length and width of the prism?


5 in. long and 5 in. wide

10 in. long and 2 in. wide

5 in. long and 4 in. wide

15 in. long and 5 in. wide



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Answer 1

A) 5 in. long and 5 in. wide

Explanation:

Given:

Volume of a rectangular prism = 75 cubic inches

Height of prism = 3 inches

Volume of a rectangular prism is given by =
`l* w* h`

where
`l` representslength of base,
`w` represents width of base and
`h` represents height of the prism.

We will check the choices given by finding the volume for the given dimensions of length and width while height remains the same and see if it matches with the given volume of the prism.

A)
`l=5\ in`
`w=5\ in`

Volume of prism =
`5* 5* 3=75\ in^3`

B)
`l=10\ in`
`w=2\ in`

Volume of prism =
`10* 2* 3=60\ in^3`

C)
`l=5\ in`
`w=4\ in`

Volume of prism =
`5* 4* 3=60\ in^3`

D)
`l=15\ in`
`w=5\ in`

Volume of prism =
`15* 5* 3=225\ in^3`

So, we see that the dimensions given in option A would give the volume of prism = 75 cubic inches.