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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #71 : Volume

A matchbox has a length of 10 inches, width of 2 inches and height of 1 inch. What is the volume of the matchbox?

Possible Answers:

20 in^3

13in^3

13 in^2

20in^2

7in^2

Correct answer:

20 in^3

Explanation:

To find the volume of a rectangular solid you must multiply the length, width, and height together.

10 * 2 * 1 = 20in^3

Volume is in units cubed.

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Example Question #12 : Volume Of A Rectangular Solid

Alfred has a fish tank that looks like this:

Rectangle volumn

Alfred needs to fill the tank with water. To do that, he needs to know the volume of the tank. Find the volume of the tank if the height is 12 inches, the length is three times the height, and the width is the same as the height.

Possible Answers:

$432 \text{ inches}^3$

$5184 \text{ inches}^3$

$1296 \text{ inches}^3$

$432 \text{ inches}^2$

$5184 \text{ inches}^2$

Correct answer:

$5184 \text{ inches}^3$

Explanation:

The fish tankbis considered a rectangular prism. The formula to find the volume of a rectangular prism is

$V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height. We know the height is 12 inches. The length is three times the height, so the length is 36 inches. The width is the same as the height, sonthe width is 12 inches. Now, we can substitute. We get

$V = 36 \text{ inches} \cdot 12 \text{ inches} \cdot 12 \text{ inches}$

$V = 5184 \text{ inches}^3$

Therefore, the volume of the fish tank is $5184 \text{ inches}^3$ .

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Example Question #72 : Volume

Find the volume of a rectangular box with the following dimensions:

Length: 4 feet. Width: 12 feet. Height: 3 feet.

Possible Answers:

24ft^3

144 ft^3

36ft^3

19ft^3

Correct answer:

144 ft^3

Explanation:

Find the volume of a rectangular box with the following dimensions:

Length: 4 feet. Width: 12 feet. Height: 3 feet.

To find volume of a rectangular box, we just need to use the following:

V=length*width*height

V=4ft*12ft*3ft=12ft*12ft^2=144ft^3

So our answer is:

144 ft^3

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Example Question #1 : Finding Volume Of A Rectangular Prism

An aquarium is shaped like a perfect cube; the perimeter of each glass face is 8.4 meters. If it is filled to the recommended $90\%$ capacity, then, to the nearest hundred cubic liters, how much water will it contain?

Possible Answers:

$9\textup,300\textup{ L}$

$8\textup,300\textup{ L}$

$4\textup,000\textup{ L}$

$4\textup,400\textup{ L}$

Insufficient information is given to answer the question.

Note: $1\textup{ cubic meter}= 1\textup{,}000\textup{ cubic liters}$

Correct answer:

$8\textup,300\textup{ L}$

Explanation:

A perfect cube has square faces; if a face has perimeter 8.4 meters, then each side of each face measures one fourth of this, or 2.1 meters. The volume of the tank is the cube of this, or

$2.1^{3} = 9.261$ cubic meters.

Its capacity in liters is $9.261 \times 1,000 = 9,261$ liters.

$90\%$ of this is

$9,261 \times 0.9 = 8,335$ liters.

This rounds to $8\textup,300$ liters, the correct response.

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Example Question #1 : Perimeter

Becky's house is surrounded by a circular lake that Becky runs around each day. If Becky wants to figure out the distance she runs around the lake, what formula should Becky use?

Possible Answers:

$P=d\Pi$

$C=\Pi r^{2}$

$C=l\cdot w$

None of the other answers

$C=2\Pi r$

Correct answer:

$C=2\Pi r$

Explanation:

Becky should use the circumfrence formula to find the distance she runs of a lake.

Correct Answer: $C=2\Pi r$

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Example Question #2 : Circumference Of A Circle

What is the circumference of a circle with an area equal to $81\pi$ ?

Possible Answers:

$9\pi$

$18\pi$

$4.5\pi$

$36\pi$

Correct answer:

$18\pi$

Explanation:

Using the area, solve for the radius:

$A=r^2\pi$

$81\pi=r^2\pi$

Divide by $\pi$ :

81=r^2

Take the square root:

$\sqrt{81}=9=r$

Plug this radius into the formula for the circumference:

$C=2r\pi=2(9)\pi=18\pi$

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Example Question #1 : Circumference Of A Circle

What is the circumference of a circle with a radius equal to ?

Possible Answers:

$196\pi$

$14\pi$

$7\pi$

$49\pi$

Correct answer:

$14\pi$

Explanation:

The circumference can be solved using the following equation:

$C=2r\pi=2(7)\pi=14\pi$

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Example Question #2 : Circumference Of A Circle

What is the circumference of a circle with a radius of ?

Possible Answers:

$16\pi$

$16\pi^{2}$

$28\pi$

$8\pi$

Correct answer:

$16\pi$

Explanation:

The circumference can be solved using the following equation:

$C=2r\pi$

Where represents the radius. Therefore, when we substitute our radius in we get:

$=2(8)\pi =16\pi$

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Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radius inches; the width of the rectangle is $8 \pi$ inches. What is the length of the rectangle?

Possible Answers:

$(30 - 8 \pi )$ inches

$44 \pi$ inches

$14 \pi$ inches

$22 \pi$ inches

$7\pi$ inches

Correct answer:

$22 \pi$ inches

Explanation:

The circumference of a circle with radius inches is

$C = 2 \pi r = 2 \pi \cdot 30 = 60 \pi$ inches.

The perimeter of the rectangle is therefore $60 \pi$ inches. To find its length, substitute $W = 8\pi$ and $P = 60\pi$ into the equation and solve for :

2 L + 2W = P

$2 L + 2 \cdot 8 \pi = 60 \pi$

$2 L + 16 \pi = 60 \pi$

$2 L + 16 \pi - 16 \pi = 60 \pi - 16 \pi$

$2 L =44 \pi$

$2 L \div 2=44 \pi \div 2$

$L = 22\pi$ inches

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Example Question #2 : Perimeter

Determine the circumference of the circle if the radius is 20.

Possible Answers:

$40\pi$

$400\pi$

$200\pi$

$20\pi$

$80\pi$

Correct answer:

$40\pi$

Explanation:

Write the formula for circumference.

$C=2\pi r$

Substitute the radius and solve.

$C=2\pi(20) = 40\pi$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #71 : Volume

Example Question #12 : Volume Of A Rectangular Solid

Example Question #72 : Volume

Example Question #1 : Finding Volume Of A Rectangular Prism

Example Question #1 : Perimeter

Example Question #2 : Circumference Of A Circle

Example Question #1 : Circumference Of A Circle

Example Question #2 : Circumference Of A Circle

Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

Example Question #2 : Perimeter

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