# ACT Math : Prisms

## Example Questions

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### Example Question #980 : Act Math

What is the surface area of a rectangular brick with a length of 12 in, a width of 8 in, and a height of 6 in?

None of the answers are correct

Explanation:

The formula for the surface area of a rectangular prism is given by:

SA = 2LW + 2WH + 2HL

SA = 2(12 * 8) + 2(8 * 6) + 2(6 * 12)

SA = 2(96) + 2(48) + 2(72)

SA = 192 + 96 + 144

SA = 432 in2

216 in2  is the wrong answer because it is off by a factor of 2

576 in3 is actually the volume, V = L * W * H

### Example Question #1 : How To Find The Volume Of A Prism

A box's length is twice as long as its width. Its height is the sum of its length and its width. What is the volume of this box if its length is 10 units?

units cubed

units cubed

units cubed

units cubed

units cubed

units cubed

Explanation:

The formula for the volume of a rectangular prism is , where "" is volume, "" is length, "" is width and "" is height.

We know that  and . By rearranging , we get . Substituting  into the volume equation for  and  into the same equation for , we get the following:

units cubed

### Example Question #2 : How To Find The Volume Of A Prism

A rectangular prism has the following dimensions:

Length:

Width:

Height:

Find the volume.

Explanation:

Given that the dimensions are: , , and  and that the volume of a rectangular prism can be given by the equation:

, where  is length,  is width, and  is height, the volume can be simply solved for by substituting in the values.

This final value can be approximated to .

### Example Question #3 : How To Find The Volume Of A Prism

A prism that is 4m by 3m by 8m has a volume of what?

Explanation:

The volume of the rectangle

so we plug in our values and obtain

.

### Example Question #5 : How To Find The Volume Of A Prism

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of , what is the area of its largest side?

21

16

12

28

49

28

Explanation:

The volume of a rectangular prism is found using the following formula:

If we substitute our known values, then we can solve for the missing side.

Divide both sides of the equation by 12.

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

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