# ISEE Upper Level Quantitative : How to find the length of an edge

## Example Questions

### Example Question #1 : How To Find The Length Of An Edge

A cube has sidelength one and one-half feet; a rectangular prism of equal volume has length 27 inches and height 9 inches. Give the width of the prism in inches.

Possible Answers:

Correct answer:

Explanation:

One and one half feet is equal to eighteen inches, so the volume of the cube, in cubic inches, is the cube of this, or

cubic inches.

The volume of a rectangular prism is

Since its volume is the same as that of the cube, and its length and height are 27 and 9 inches, respectively,  we can rewrite this as

The width is 24 inches.

### Example Question #1 : How To Find The Length Of An Edge

A cube has sidelength one and one-half feet; a rectangular prism of equal surface area has length 27 inches and height 9 inches. Give the width of the prism in inches.

Possible Answers:

Correct answer:

Explanation:

One and one half feet is equal to eighteen inches, so the surface area of the cube, in square inches, is six times the square of this, or

square inches.

The surface area of a rectangular prism is determined by the formula

.

So, with substitutiton, we can find the width:

inches

### Example Question #3 : How To Find The Length Of An Edge

A rectangular prism has volume one cubic foot; its length and width are, respectively, 9 inches and  inches. Which of the following represents the height of the prism in inches?

Possible Answers:

Correct answer:

Explanation:

The volume of a rectangular prism is the product of its length, its width, and its height. The prism's volume of one cubic foot is equal to  cubic inches.

Therefore,  can be rewritten as .

We can solve for  as follows: