GMAT Math : Prisms

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Example Question #1 : Prisms

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.

Possible Answers:

$\small 9,988 \; ft ^{2}$

$\small 7,683 \; ft ^{2}$

$\small 10,756 \; ft ^{2}$

$\small 9,220 \; ft ^{2}$

$\small 5,378 \; ft ^{2}$

Correct answer:

$\small 7,683 \; ft ^{2}$

Explanation:

450,000 gallons of water occupy $\small \small 0.1337 \cdot 450,000 \approx 60,165$ cubic feet.

Let $\small h$ be the height of the tank. Then the width of the tank is W = 2H , and its length is L = 2W = 4H . Multiply the dimensions to get the volume:

$V = LWH = H \cdot 2H\cdot 4H = 8H^{3} = 60,165$

$H^{3} = 60,165 \div 8 \approx 7,521$

$H = \sqrt[3]{7,521} \approx 19.6$

$W = 2H = 2 \cdot19.6 = 39.2$

$L = 2W = 2\cdot 39.2 = 78.4$

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

A = 2LH + 2WH + LW

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2$

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2 \approx 7,683$

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

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Example Question #2 : Prisms

A rectangular prism has a volume of 105 . If the length of the prism is and its width is , what is its height?

Possible Answers:

$\frac{5}{2}$

$\frac{3}{2}$

Correct answer:

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:

V=LWH

105=(7)(5)H

$H=\frac{105}{35}=3$

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Example Question #1 : 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?

Possible Answers:

$\frac{7}{2}$

Correct answer:

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:

V=LWH

70=(7)W(2)

70=14W

$W=\frac{70}{14}=5$

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Example Question #41 : Rectangular Solids & Cylinders

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

Possible Answers:

Correct answer:

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:

SA=2LW+2LH+2WH

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

92=2L(3)+2L(2)+2(3)(2)

92=6L+4L+12

10L=80

L=8

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Example Question #1 : Prisms

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 294 square inches of material.

II) The cube will hold 343 cubic inches.

Possible Answers:

Both statements are needed to answer the question.

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

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

Neither statement is sufficient to answer the question. More information is needed.

Either statement is sufficient to answer the question.

Correct answer:

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,

$SA=6\cdot s^2$

$294=6s^2 \rightarrow 49=s^2 \rightarrow 7=s$ .

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

V=s^3

$343=s^3 \rightarrow 7=s$

Either can be used to find the side length.

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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?

Possible Answers:

154

148

112

120

172

Correct answer:

148

Explanation:

SA=2lw+2lh+2hw=2*4*6+2*4*5+2*5*6=48+40+60=148

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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:

$\$34$

$\$17$

$\$20$

$\$40$

Correct answer:

$\$34$

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.

$2(80)+2(40)+2(50)=340\ in^{2}$

Since the price is $.10 for each square inch,

$Total\ cost=340(.10)=\$34$

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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?

Possible Answers:

$22,464 \textrm{ cm}^{2}$

$7,672 \textrm{ cm}^{2}$

$25,872 \textrm{ cm}^{2}$

$5,856 \textrm{ cm}^{2}$

$6,104 \textrm{ cm}^{2}$

Correct answer:

$5,856 \textrm{ cm}^{2}$

Explanation:

Let be the height of the prism. Then the width is , and the length is 3h+ 16 . Since the sum of the three dimensions is one meter, or 100 centimeters, we solve for in this equation:

h + 3h + (3h+16) = 100

7h+16 = 100

7h+16-16 = 100-16

7h = 84

$7h \div 7 = 84 \div 7$

h = 12

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 l= 52,w=36,h=12 in the formula for the surface area of a rectangular prism:

A = 2lw + 2wh + 2lh

$= 2 \cdot 52 \cdot 36 + 2 \cdot 36 \cdot 12 + 2 \cdot 52 \cdot 12$

= 3,744 + 864 + 1,248

= 5,856 square centimeters

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Example Question #1 : 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?

Possible Answers:

Correct answer:

Explanation:

We can set the lengths of three sides to be , , , respectively. The volume is 120 means that xyz=120 . 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

xy * xz * yz = x^2 * y^2 * z^2 =(xyz)^2 to solve .

20 * 30 * yz = 120^2

yz=24

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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.

Possible Answers:

1,152

2,304

1,344

768

584

Correct answer:

1,344

Explanation:

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

$\frac{1}{2} \cdot 12 \cdot 16 = 96$

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

$c = \sqrt{12^{2}+16^{2}}= \sqrt{144+256} = \sqrt{400}= 20$

Therefore, the perimeter of each base is

P=12+16+20 = 48 ,

and the height of the prism is half this, or $h = \frac{1}{2} \cdot 48 = 24$ .

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

$L= Ph= 24 \cdot 48 = 1,152$

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

S= L+B+B =1,152+96+96 =1,344 .

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GMAT Math : Prisms

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Prisms

Example Question #2 : Prisms

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

Example Question #41 : Rectangular Solids & Cylinders

Example Question #1 : Prisms

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

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

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

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

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

All GMAT Math Resources

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