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Common Core: 7th Grade Math : Geometry

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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All Common Core: 7th Grade Math Resources

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Example Questions

Example Question #1 : Volume Of A Rectangular Solid

If a cube is inches tall, what is its volume?

Possible Answers:

Not enough information provided.

500

512

384

Correct answer:

512

Explanation:

To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla $v=l\cdot w\cdot h$ . Since a cube has equal sides, we can use for all three values.

$8\cdot 8\cdot 8=512\: in ^{3}$

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Example Question #2 : Volume Of A Rectangular Solid

What is the volume of a cube with a side length equal to inches?

Possible Answers:

$343\: in^{3}$

$53\: in^{3}$

$21\: in^{3}$

$49\: in^{3}$

Correct answer:

$343\: in^{3}$

Explanation:

The volume of a a cube (or rectangular prism) can be solved using the following equation:

$V=l\times\ w\times\ h$

$V=7in\times 7in\times 7in=343in^3$

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Example Question #1 : Finding Volume Of A Cube

Give the volume of a cube with surface area 150 square inches.

Possible Answers:

$250\textup{ in}^{3}$

$250\sqrt{3}\textup{ in}^{3}$

$125\textup{ in}^{3}$

$375\textup{ in}^{3}$

$125\sqrt{3}\textup{ in}^{3}$

Correct answer:

$125\textup{ in}^{3}$

Explanation:

Let be the length of one edge of the cube. Since its surface area is 150 square inches, one face has one-sixth of this area, or $\frac{150}{6} = 25$ square inches. Therefore, $s^{2} = 25$ , and s = 5 .

The volume is the cube of this, or $V= 5^{3}=125$ cubic inches.

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Example Question #1 : Finding Volume Of A Cube

Give the volume of a cube with surface area 240 square inches.

Possible Answers:

$120 \sqrt{10} \textup{ in}^{3}$

$80 \sqrt{10} \textup{ in}^{3}$

$120 \textup{ in}^{3}$

$80 \textup{ in}^{3}$

$40 \sqrt{10} \textup{ in}^{3}$

Correct answer:

$80 \sqrt{10} \textup{ in}^{3}$

Explanation:

Let be the length of one edge of the cube. Since its surface area is 240 square inches, one face has one-sixth of this area, or $\frac{240}{6} = 40$ square inches. Therefore, $s^{2} = 40$ , and $s = \sqrt{40} = 2\sqrt{10}$ .

The volume is the cube of this, or $V= \left ( 2\sqrt{10} \right )^{3}= 2^{3} \cdot \left ( \sqrt{10} \right )^{3}= 8 \cdot 10 \sqrt{10}= 80 \sqrt{10}$ cubic inches.

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Example Question #2 : Finding Volume Of A Cube

Calculate the volume of the provided figure.

Possible Answers:

$343\textup{ in}^3$

$345\textup{ in}^3$

$344\textup{ in}^3$

$341\textup{ in}^3$

$342\textup{ in}^3$

Correct answer:

$343\textup{ in}^3$

Explanation:

In order to solve this problem, we need to recall the volume formula for a cube:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=7\times7\times7$

$V=343\textup{ in}^3$

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Example Question #3 : Finding Volume Of A Cube

Calculate the volume of the provided figure.

Possible Answers:

$216\textup{ in}^3$

$212\textup{ in}^3$

$215\textup{ in}^3$

$214\textup{ in}^3$

$213\textup{ in}^3$

Correct answer:

$216\textup{ in}^3$

Explanation:

In order to solve this problem, we need to recall the volume formula for a cube:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=6\times6\times6$

$V=216\textup{ in}^3$

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Example Question #4 : Finding Volume Of A Cube

Calculate the volume of the provided figure.

Possible Answers:

$1\textup,332\textup{ in}^3$

$1\textup,333\textup{ in}^3$

$1\textup,335\textup{ in}^3$

$1\textup,334\textup{ in}^3$

$1\textup,331\textup{ in}^3$

Correct answer:

$1\textup,331\textup{ in}^3$

Explanation:

In order to solve this problem, we need to recall the volume formula for a cube:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=11\times11\times11$

$V=1\textup,331\textup{ in}^3$

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Example Question #1 : Area Of A Circle

What is the area of a circle that has a diameter of inches?

Possible Answers:

940

706.8583

960

176.7146

153.938

Correct answer:

176.7146

Explanation:

The formula for finding the area of a circle is $\pi r^{2}$ . In this formula, represents the radius of the circle. Since the question only gives us the measurement of the diameter of the circle, we must calculate the radius. In order to do this, we divide the diameter by .

$\frac{15}{2}=7.5$

Now we use 7.5 for in our equation.

$\pi (7.5)^{2}=176.7146 \: in^{2}$

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Example Question #1 : Area Of A Circle

What is the area of a circle with a diameter equal to 6?

Possible Answers:

$3\pi$

$9\pi$

$36\pi$

$18\pi$

Correct answer:

$9\pi$

Explanation:

First, solve for radius:

$r=\frac{d}{2}=\frac{6}{2}=3$

Then, solve for area:

$A=r^2\pi=3^2\pi=9\pi$

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Example Question #931 : Grade 7

The diameter of a circle is $4\ cm$ . Give the area of the circle.

Possible Answers:

$12.56\ cm^2$

$12 \ cm^2$

$11.56\ cm^2$

$13.56\ cm^2$

$13\ cm^2$

Correct answer:

$12.56\ cm^2$

Explanation:

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle, and $\pi$ is approximately 3.14 .

$Area=\frac{\pi d^2}{4}=\frac{\pi\times 4^2}{4}=4\pi \Rightarrow Area\approx 4\times 3.14\Rightarrow Area\approx 12.56 \ cm^2$

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Common Core: 7th Grade Math : Geometry

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #1 : Volume Of A Rectangular Solid

Example Question #2 : Volume Of A Rectangular Solid

Example Question #1 : Finding Volume Of A Cube

Example Question #1 : Finding Volume Of A Cube

Example Question #2 : Finding Volume Of A Cube

Example Question #3 : Finding Volume Of A Cube

Example Question #4 : Finding Volume Of A Cube

Example Question #1 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #931 : Grade 7

All Common Core: 7th Grade Math Resources

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