# GMAT Math : Prisms

## Example Questions

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### Example Question #1 : Calculating The Length Of An Edge Of A Prism

A new fish tank at a theme park must hold 450,000 gallons of sea water. Its dimensions must be such that it is twice as long as it is wide, and half as high as it is wide. If one gallon of water occupies 0.1337 cubic feet, then give the surface area of the proposed tank to the nearest square foot.

You may assume that the tank has all four sides and a bottom, but is open at the top.

Explanation:

450,000 gallons of water occupy  cubic feet.

Let  be the height of the tank. Then the width of the tank is , and its length is . Multiply the dimensions to get the volume:

Since the tank has four sides and a bottom, but not a top, its surface area is

The surface area of the tank is about 7,683 square feet.

### Example Question #2 : Calculating The Length Of An Edge Of A Prism

A rectangular prism has a volume of .  If the length of the prism is  and its width is , what is its height?

Explanation:

The volume of a rectangular prism is equal to its length times its width times its height. We are given the volume, the length, and the width, so using the following formula we can solve for the height of the rectangular prism:

### Example Question #3 : Calculating The Length Of An Edge Of A Prism

A rectangular prism has a volume of  ,  a length of  ,  and a height of  .  What is the width of the prism?

Explanation:

Using the formula for the volume of a rectangular prism, we can plug in the given values and solve for the width of the prism:

### Example Question #4 : Calculating The Length Of An Edge Of A Prism

A rectangular prism has a surface area of  ,  a width of  ,  and a height of  .  What is the length of the prism?

Explanation:

We are given the surface area and the length of two sides, so in order to calculate the length of the third side we need the formula for the surface area of a prism in terms of each side length:

Using the formula, we can simply plug in the given values and solve for the length of the rectangular prism:

### Example Question #5 : Calculating The Length Of An Edge Of A Prism

Jenny wants to make a cube out of sheet metal. What is the length of one side of the cube?

I) The cube will require  square inches of material.

II) The cube will hold  cubic inches.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Both statements are needed to answer the question.

Either statement is sufficient to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Explanation:

The length of an edge of a cube can be used to find either volume or surface area, and vice versa.

I) Gives us the surface area thus, we are able to calculate the length of an edge using the formula,

.

II) Gives us the volume thus, we are able to calculate the length of an edge using the formula,

Either can be used to find the side length.

### Example Question #1 : Calculating The Surface Area Of A Prism

What is the surface area of a rectangular prism that is 4 inches long, 6 inches wide, and 5 inches high?

Explanation:

### Example Question #2 : Calculating The Surface Area Of A Prism

A box with dimensions 8 inches, 10 inches, and 5 inches needs to be gift wrapped. Gift wrapping is priced at $0.10 per square inch of surface of a box. How much will it cost to wrap the gift? Possible Answers: Correct answer: Explanation: Find the surface area of the box by summing the area of all six faces: two 8 by 10, two 8 by 5, two 10 by 5. Since the price is$.10 for each square inch,

### Example Question #3 : Calculating The Surface Area Of A Prism

The sum of the length, the width, and the height of a rectangular prism is one meter. The length of the prism is sixteen centimeters greater than its width, which is three times its height. What is the surface area of this prism?

Explanation:

Let  be the height of the prism. Then the width is , and the length is . Since the sum of the three dimensions is one meter, or 100 centimeters, we solve for  in this equation:

The height of the prism is 12 cm; the width is three times this, or 36 cm; the length is sixteen centimeters greater than the width, which is 52 cm.

Set   in the formula for the surface area of a rectangular prism:

square centimeters

### Example Question #4 : Calculating The Surface Area Of A Prism

The volume of the rectangular solid above is 120. The area of ABFE is 20 and the area of ABCD is 30. What is the area of BFGC?

Explanation:

We can set the lengths of three sides to be , , , respectively. The volume is 120 means that . Also we know the areas of two sides, so we can use  to represent the area of 20 and  to represent the area of 30. Now the question is to figure out . Then we can use

to solve .

### Example Question #5 : Calculating The Surface Area Of A Prism

A right prism has as its bases two right triangles, each of whose legs have lengths 12 and 16. The height of the prism is half the perimeter of a base. Give the surface area of the prism.

Explanation:

The area of a right triangle is equal to half the product of its legs, so each base has area

The measure of the hypotenuse of each base is determined using the Pythagorean Theorem:

Therefore, the perimeter of each base is

,

and the height of the prism is half this, or .

The lateral area of the prism is the product of its height and the perimeter of a base; this is

The surface area is the sum of the lateral area and the two base areas, or

.

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