GMAT Math : Geometry

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Example Questions

Example Question #34 : Rectangular Solids & Cylinders

Daisy has an empty cylindrical water bottle that has a radius of 3cm and a height of 15cm . How much water can she add to the bottle to fill it up?

Possible Answers:

$180\pi cm^{3}$

$45\pi cm^{3}$

Not enough information provided

$135\pi cm^{3}$

$18\pi cm^{3}$

Correct answer:

$135\pi cm^{3}$

Explanation:

Since we are looking to find out how much water the bottle can hold, we need to find the volume of the bottle. The volume of a cylinder with radius and height is defined as $V=\pi r^{2}h$ . Plugging in our given values:

$V=\pi (3cm)^{2}(15cm)$

$V=\pi (9cm^{2})(15cm)$

$V=135\pi cm^{3}$

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Example Question #521 : Geometry

Find the volume of a cylinder whose height is and radius is .

Possible Answers:

$\24\pi$

$32\pi$

$8\pi$

$16\pi$

Correct answer:

$32\pi$

Explanation:

To find the volume of a cylinder, you must use the following equation:

$V=\pi{r^2}h$

Thus,

$V=\pi(2^2)(8)=32\pi$

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Example Question #522 : Geometry

Find the volume of a cylinder whose height is and radius is .

Possible Answers:

$81\pi$

$9\pi$

$27\pi$

$64\pi$

Correct answer:

$81\pi$

Explanation:

To find the volume, you must use the following formula.

$V=\pi{r^2}h=\pi(3^2)(9)=81\pi$

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Example Question #762 : Problem Solving Questions

The height of a cylinder is $\pi ^{x}$ ; its bases are circles with radius $\pi$ .

Give the volume of the cylinder.

Possible Answers:

$\pi ^{x+3}$

$\pi ^{2x+2}$

$\pi ^{x+2}$

$\pi ^{2x+3}$

$\pi ^{2x+1}$

Correct answer:

$\pi ^{x+3}$

Explanation:

The volume of a cylinder can be calculated from its radius and height as follows:

$V = \pi r ^{2} h$

Setting $h = \pi ^{x}$ and $r = \pi$ .

$V = \pi \cdot \pi ^{2} \cdot \pi ^{x} = \pi^{1} \cdot \pi ^{2} \cdot \pi ^{x} = \pi ^{1+2+x} = \pi ^{x+3}$

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Example Question #763 : Problem Solving Questions

A right circular cylinder has bases of radius $\pi ^{x}$ ; its height is $\pi ^{y}$ . Give its volume.

Possible Answers:

$\pi^{ x+y+1}$

$\pi ^{ 2x+1 } + \pi ^{x+y+1}$

$\pi^{2 x+y+1}$

$\pi ^{ 2y+1 } + \pi ^{x+y+1}$

$\pi^{ x+2y+1}$

Correct answer:

$\pi^{2 x+y+1}$

Explanation:

The volume of a cylinder can be calculated from its radius and height as follows:

$V = \pi r ^{2} h$

Setting $r = \pi^{x}$ and $h = \pi ^{x}$ :

$V = \pi \cdot (\pi^{x}) ^{2} \cdot \pi^{y}$

$V = \pi^{1} \cdot \pi^{2 x} \cdot \pi^{y}$

$V = \pi^{1+2 x+y}$ or $V = \pi^{2 x+y+1}$

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Example Question #13 : Calculating The Volume Of A Cylinder

Find the volume of a cylinder whose diameter is and height is .

Possible Answers:

$25\pi$

$96\pi$

$24\pi$

$10\pi$

Correct answer:

$24\pi$

Explanation:

To solve, you must use the following equation:

$V=\pi{r^2}h$ , given r=2 and h=6 . Thus,

$V=\pi(2^2)(6)=24\pi$

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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.

Possible Answers:

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

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

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

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

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

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 : Calculating The Length Of An Edge Of A Prism

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 #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?

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 #4 : Prisms

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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GMAT Math : Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #34 : Rectangular Solids & Cylinders

Example Question #521 : Geometry

Example Question #522 : Geometry

Example Question #762 : Problem Solving Questions

Example Question #763 : Problem Solving Questions

Example Question #13 : Calculating The Volume Of A Cylinder

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

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

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

Example Question #4 : Prisms

All GMAT Math Resources

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