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HSPT Math : Geometry

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Example Questions

Example Question #54 : Quadrilaterals

Swimming_pool

The above depicts a rectangular swimming pool for an apartment. The pool is two meters deep everywhere. What is the volume of the pool in cubic meters?

Possible Answers:

$720 \textrm{ m}^{3}$

$876\textrm{ m}^{3}$

The correct answer is not among the other choices.

$820\textrm{ m}^{3}$

$1,440\textrm{ m}^{3}$

Correct answer:

$720 \textrm{ m}^{3}$

Explanation:

The pool can be seen as a rectangular prism with dimensions 24 meters by 15 meters by 2 meters; its volume is the product of these dimensions, or

$24 \times 15 \times 2 = 720$ cubic meters.

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Example Question #2 : How To Find The Volume Of A Figure

A cheese seller has a 2 foot x 2 foot x 2 foot block of gouda and she wants to cut it into smaller gouda cubes that are 1.5 inches on a side. How many cubes can she cut?

Possible Answers:

4096

2048

512

256

1024

Correct answer:

4096

Explanation:

First we need to determine how many of the small cubes of gouda would fit along one dimension of the large cheese block. One edge of the large block is 24 inches, so 16 smaller cubes $(24\div 1.5)$ would fit along the edge. Now we simply cube this one dimension to see how many cubes fit within the whole cube. $16^{3}=4096$ .

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Example Question #3 : How To Find The Volume Of A Figure

An aquarium is shaped like a perfect cube; the area of each glass face is 1.44 square meters. If it is filled to the recommended 90% capacity, then, to the nearest hundred liters, how much water will it contain?

Note: 1 cubic meter = 1,000 liters.

Possible Answers:

$1,400\textup{ L}$

$1,700\textup{ L}$

$1,200\textup{ L}$

$1,600 \textup{ L}$

$1,300\textup{ L}$

Correct answer:

$1,600 \textup{ L}$

Explanation:

A perfect cube has square faces; if a face has area 1.44 square meters, then each side of each face measures the square root of this, or 1.2 meters. The volume of the tank is the cube of this, or

$1.2^{3} = 1.728$ cubic meters.

Its capacity in liters is $1.728 \times 1,000 = 1,728$ liters.

90% of this is

$1,728 \times 0.9 = 1,555.2$ liters.

This rounds to 1,600 liters, the correct response.

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Example Question #2 : How To Find The Volume Of A Figure

Chemicals to clean a swimming pool cost $0.24 per cubic foot of water. If a pool is 6 feet deep, 14 feet long and 8 feet wide, how much does it cost to clean the pool? Round to the nearest dollar.

Possible Answers:

$\$150$

$\$161$

$\$202$

$\$672$

$\$184$

Correct answer:

$\$161$

Explanation:

The volume of the pool can be determined by multiplying the length, width, and height together.

$V = 6 \times 8 \times 14 = 672 ft^{3}$

Each cubit foot costs 24 cents, so:

$672ft^3\times \$0.24=\$161.28\approx \$161$

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Example Question #31 : Solid Geometry

The density of gold is $16\ g/cm^3$ and the density of glass is $2\ g/cm^3$ . You have a gold cube that is $x\ cm$ in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?

Possible Answers:

1.5x

2.5x

Correct answer:

Explanation:

Weight = Density * Volume

Volume of Gold Cube = side³= x³

Weight of Gold = 16 g/cm³* x³

Weight of Glass = 3/cm³ * side³

Set the weight of the gold equal to the weight of the glass and solve for the side length:

16* x³ = 2 * side³

side³ = 16/2* x³= 8 x³

Take the cube root of both sides:

side = 2x

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Example Question #2 : How To Find The Volume Of A Figure

What is the volume of a cylinder with a diameter of 6, and a height of 5?

Possible Answers:

$180\pi$

$30\pi$

$45\pi$

$15\pi$

$90\pi$

Correct answer:

$45\pi$

Explanation:

Write the formula to find the volume of a cylinder.

$V=\pi r^2 h$

The radius is half the diameter, which is 3.

Substitute all the known dimensions into the formula.

$V=\pi( 3^2) (5)=45\pi$

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Example Question #2 : How To Find The Volume Of A Figure

Find the volume of the cube if the face of square has a perimeter of $\textup{4 units}$ .

Possible Answers:

$64\textup{{ units}}^{3}$

$6\textup{{ units}}^{3}$

$1\textup{{ units}}^{3}$

$16\textup{{ units}}^{3}$

$8\textup{{ units}}^{3}$

Correct answer:

$1\textup{{ units}}^{3}$

Explanation:

Find the side length of the square given the square perimeter. The perimeter of a square is:

P=4s

4=4s

s=1

The side of the cube has a length of one.

Write the formula to find the volume of a cube.

V=s^3

Substitute the side length.

$V=s^3= (1)^3=1\textup{ units}^{3}$

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Example Question #3 : How To Find The Volume Of A Figure

Swimming_pool

One cubic meter is equal to one thousand liters.

The above depicts a rectangular swimming pool for an apartment. The pool is 2.5 meters deep everywhere. How many liters of water does the pool hold?

Possible Answers:

$1,950,000\textrm{ L}$

$195,000\textrm{ L}$

$9,000,000\textrm{ L}$

$90,000\textrm{ L}$

$900,000\textrm{ L}$

Correct answer:

$900,000\textrm{ L}$

Explanation:

The pool can be seen as a rectangular prism with dimensions meters by meters by 2.5 meters; its volume in cubic meters is the product of these dimensions, which is

$24 \times 15 \times 2.5 = 900$ cubic meter.

One cubic meter is equal to one thousand liters, so multiply:

$900 \times 1,000 = 900,000$ liters of water.

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Example Question #3 : How To Find The Volume Of A Figure

What is the volume of the rectangular prism below?

Screen shot 2015 11 05 at 12.01.48 pm

Possible Answers:

110cm^3

90cm^3

100cm^3

47cm^3

45cm^3

Correct answer:

90cm^3

Explanation:

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=9\times\2\times5$

$\small v=90cm^3$

Remember, volume is always labeled as units to the third power.

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Example Question #261 : Measurement & Data

What is the volume of the rectangular prism below?

Screen shot 2015 11 05 at 12.00.31 pm

Possible Answers:

30cm^3

35cm^3

15cm^3

40cm^3

45cm^3

Correct answer:

30cm^3

Explanation:

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=5\times\2\times3$

$\small v=30cm^3$

Remember, volume is always labeled as units to the third power.

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #54 : Quadrilaterals

Example Question #2 : How To Find The Volume Of A Figure

Example Question #3 : How To Find The Volume Of A Figure

Example Question #2 : How To Find The Volume Of A Figure

Example Question #31 : Solid Geometry

Example Question #2 : How To Find The Volume Of A Figure

Example Question #2 : How To Find The Volume Of A Figure

Example Question #3 : How To Find The Volume Of A Figure

Example Question #3 : How To Find The Volume Of A Figure

Example Question #261 : Measurement & Data

All HSPT Math Resources

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