### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : Solid Geometry

Which is the greater quantity?

(a) The sidelength of a cube with surface area

(b) The sidelength of a cube with volume

**Possible Answers:**

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

(b) is greater

**Correct answer:**

(a) and (b) are equal

(a) A cube has six faces, each a square. Since the surface area of this cube is , each face has one-sixth this area, or ; the sidelength is the square root of this, or .

(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:

The cubes have the same sidelength.

### Example Question #2 : Solid Geometry

Which is the greater quantity?

(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters

(b) The volume of a cube with sidelength 300 millimeters

**Possible Answers:**

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

**Correct answer:**

(a) and (b) are equal

(a) The volume of the prism is the product of its length, its width, and its height:

(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:

The volumes are equal.