GMAT Math : Calculating the volume of a prism

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Example Question #1 : Calculating The Volume Of A Prism

A cube of iron has a mass of 4 kg. What is the mass of a rectangular prism of iron that is the same height but has a width and length that are twice as long as the cube?

Possible Answers:

Correct answer:

Explanation:

Let the length of the sides of the cube equal 1. The volume of the cube is then $\dpi{100} 1\times 1\times 1=1$ . Therefore, the volume of the prism is $\dpi{100} 2\times 2\times 1=4$ . Therefore, the mass of the prism must be 4 times greater than the mass of the cube.

$\small (4)(4)=\ 16$

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Example Question #2 : Calculating The Volume Of A Prism

What is the volume of a cube whose diagonal measures 10 inches?

Possible Answers:

$333.3 \;in^{3}$

$100\; in ^{3}$

$353.6\;in^{3}$

$1,000\; in ^{3}$

$192.5\; in ^{3}$

Correct answer:

$192.5\; in ^{3}$

Explanation:

By an extension of the Pythagorean Theorem, if is the length of an edge of the cube and is its diagonal length,

$d^{2}= s^{2}+s^{2}+s^{2} = 3s^{2}$

$\sqrt{3s^{2} }= \sqrt{d^{2}}$

$s\sqrt{3 }= d$

$s= \frac{d}{\sqrt{3 }}$

The volume is therefore

$V = s^{3} = \left (\frac{d}{\sqrt{3}} \right )^{3} = \left (\frac{10}{\sqrt{3}} \right )^{3}\approx 192.5$

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Example Question #2 : Calculating The Volume Of A Prism

The length, width, and height of a rectangular prism, in inches, are three different prime numbers. All three dimensions are between one yard and four feet. What is the volume of the prism?

Possible Answers:

$74,777\textrm{ in}^{3}$

$65,231\textrm{ in}^{3}$

It is impossible to tell from the information given.

$71,299\textrm{ in}^{3}$

$82,861\textrm{ in}^{3}$

Correct answer:

It is impossible to tell from the information given.

Explanation:

One yard is equal to 36 inches; four feet are equal to 48 inches. There are four prime numbers between 36 and 48 - 37, 41, 43, and 47. Since we are only given that the dimensions are three different prime numbers between 36 and 48, we have no way of knowing which three they are.

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Example Question #781 : Gmat Quantitative Reasoning

A company makes cubic metal blocks whose edges measure 5 inches. The blocks are supposed to be packed in crates 40 inches long, 30 inches wide, and 32 inches high. How many blocks can be packed in one of these crates?

Possible Answers:

307

288

240

336

308

Correct answer:

288

Explanation:

Each layer of blocks will be $40 \div 5 = 8$ blocks long and $30 \div 5 = 6$ blocks wide, making a layer of $8 \times 6 = 48$ blocks. The height is 32 feet, which divided by 5 is

$32 \div 5 = 6\textrm{ R }2$

so there will be 6 layers of blocks.

Therefore, $48 \times 6 = 288$ blocks can be packed.

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Example Question #5 : Calculating The Volume Of A Prism

The sum of the length, the width, and the height of a rectangular prism is one yard. The length of the prism is eleven inches greater than its width, and the width is twice its height. What is the volume of the prism?

Possible Answers:

$2,150 \textrm{ in}^{3}$

$2,450 \textrm{ in}^{3}$

$3,150 \textrm{ in}^{3}$

$1,750 \textrm{ in}^{3}$

$1,050 \textrm{ in}^{3}$

Correct answer:

$1,050 \textrm{ in}^{3}$

Explanation:

Let be the height of the prism. Then the width is , and the length is 2h+ 11 . Since the sum of the three dimensions is one yard, or 36 inches, we solve for in this equation:

h + 2h + (2h+11) = 36

5h+11 = 36

5h+11 -11 = 36-11

5h = 2 5

$5h \div 5 = 25 \div 5$

h = 5

The height is 5 inches; the width is twice this, or 10 inches; the length is eleven inches greater than the width, or 21 inches. The volume is the product of the three dimensions:

$V = lwh = 5 \cdot10\cdot21 = 1,050$ cubic inches.

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Example Question #6 : Calculating The Volume Of A Prism

A given cylinder has circular bases of radius and height . What is the volume of the cylinder?

Possible Answers:

$72\pi$

$18\pi$

$144\pi$

$36\pi$

$432\pi$

Correct answer:

$432\pi$

Explanation:

The volume of a given cylinder is the product of its base area (A) and height (h) , or V=Ah . Since the circular base area $A=\pi r^{2}$ , we can substitute and plug in the values provided:

V=Ah

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

$V=(\pi (6)^{2})(12)$

$V=432\pi$

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Example Question #7 : Calculating The Volume Of A Prism

A given rectangular prism has a length of 7cm , a width of 5cm , and a height of 9cm . What is the volume of the prism?

Possible Answers:

Not enough information provided.

$21cm^{3}$

$315cm^{3}$

$108cm^{3}$

$52cm^{3}$

Correct answer:

$315cm^{3}$

Explanation:

The volume of a given rectangular prism is the product of its length (l) , width (w) , and height (h) , or V=lwh . Plugging in the values provided:

V=(7cm)(5cm)(9cm)

$V=315cm^{3}$

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Example Question #8 : Calculating The Volume Of A Prism

A given rectangular prism has a length of 10cm , a width of 5cm , and a height of 20cm . What is its volume?

Possible Answers:

$100cm^{3}$

$1000cm^{3}$

$700cm^{3}$

$500cm^{3}$

$35cm^{3}$

Correct answer:

$1000cm^{3}$

Explanation:

The volume of a given rectangular prism is the product of its length (l) , width (w) , and height (h) , or V=lwh . Plugging in the values provided:

V=(10cm)(5cm)(20cm)

$V=1000cm^{3}$

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Example Question #3 : Calculating The Volume Of A Prism

Ron is making a wooden chest. The chest needs to measure 45 inches by 72 inches by 36 inches. What volume will the chest be able to hold in cubic feet?

Possible Answers:

153

67.5

$116\textup{,}640$

Correct answer:

67.5

Explanation:

Because we are asked for an answer in cubic feet, convert all measurments to feet right away

45 inches: 3.5 feet

72 inches: 6 feet

36 inches: 3 feet

Volume of a rectangular prism is given by:

V=l*w*h

V=3*6*3.5=67.5 ft^3

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GMAT Math : Calculating the volume of a prism

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating The Volume Of A Prism

Example Question #2 : Calculating The Volume Of A Prism

Example Question #2 : Calculating The Volume Of A Prism

Example Question #781 : Gmat Quantitative Reasoning

Example Question #5 : Calculating The Volume Of A Prism

Example Question #6 : Calculating The Volume Of A Prism

Example Question #7 : Calculating The Volume Of A Prism

Example Question #8 : Calculating The Volume Of A Prism

Example Question #3 : Calculating The Volume Of A Prism

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