Question

A right square prism has a volume of 360 cubic units. Which could be the dimensions, in units, of the prism? Check all that apply. 3 by 3 by 40 4 by 4 by 20 6 by 6 by 10 2.5 by 12 by 12 3.6 by 10 by 10

Answer 1

First Option 3 by 3 by 40

Fourth Option 2.5 by 12 by 12

Fifth Option 3.6 by 10 by 10

Answer 2

The correct choices are:

A. 3 by 3 by 40

C. 6 by 6 by 10

D. 2.5 by 12 by 12

E. 3.6 by 10 by 10

Explanation:

A right square prism is a box which has at least one pair of opposite faces that are squares. it's volume is:

`V=x^2h.`

So from our choices we want to check if at least two of the dimensions have equal length, and whether the volume amounts to 360 cubic units.

Let us check each of the choices one by one.

Choice A: 3 by 3 by 40.

At least two sides are identical and the volume
`v=3*3*40=360` cubic units. Therefore this choice is correct.

Choice B: 4 by 4 by 20.

At least two sides are equal, but the volume
`V=4*4*20\\eq 360` cubic units. Therefore this choice is incorrect.

Choice C: 6 by 6 by 10.

At least two sides are equal and the volume
`V=6*6*10= 360` cubic units. Therefore this choice is correct.

Choice D: 2.5 by 12 by 12.

At least two sides are equal and the volume
`V=2.5*12*12= 360` cubic units. Therefore this choice is correct.

Choice E: 3.6 by 10 by 10.

At least two sides are equal and the volume
`V=3.6*10*10= 360` cubic units. Therefore this choice is correct.

Thus, only choices A, C, D, and E are correct.