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Common Core: 7th Grade Math : Grade 7

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 : How To Find The Volume Of A Cube

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

Possible Answers:

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

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

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

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

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

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:

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

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

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

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

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

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 #931 : Grade 7

Calculate the volume of the provided figure.

Possible Answers:

$344\textup{ in}^3$

$341\textup{ in}^3$

$345\textup{ in}^3$

$342\textup{ in}^3$

$343\textup{ in}^3$

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 #1 : Finding Volume Of A Cube

Calculate the volume of the provided figure.

Possible Answers:

$213\textup{ in}^3$

$216\textup{ in}^3$

$214\textup{ in}^3$

$215\textup{ in}^3$

$212\textup{ in}^3$

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 #3 : Finding Volume Of A Cube

Calculate the volume of the provided figure.

Possible Answers:

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

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

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

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

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

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:

960

153.938

706.8583

153.938

176.7146

960

940

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

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

Possible Answers:

$9\pi$

$3\pi$

$36\pi$

$18\pi$

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 #171 : Plane Geometry

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

Possible Answers:

$13.56\ cm^2$

$11.56\ cm^2$

$12 \ cm^2$

$13\ cm^2$

$12.56\ cm^2$

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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Example Question #11 : Area And Circumference Of A Circle

The diameter of a circle is . Give the area of the circle in terms of .

Possible Answers:

12.56 t^2

12 t^2

11.56 t

12.56 t

11.56 t^2

Correct answer:

12.56 t^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 .

$Area=\frac{\pi (4t)^2}{4}=\frac{16\pi t^2}{4}=4\pi t^2 \Rightarrow Area\approx 4\times 3.14\times t^2$

$\Rightarrow Area\approx 12.56t^2$

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Example Question #3 : How To Find The Area Of A Circle

The radius of a circle is $\frac{2}{\sqrt{\pi }}$ . Give the area of the circle.

Possible Answers:

$4\pi$

$2\pi$

$\frac{4}{\pi }$

Correct answer:

Explanation:

The area of a circle can be calculated as $Area=\pi r^2$ , where is the radius of the circle, and $\pi$ is approximately 3.14 .

$Area=\pi r^2=\pi\times (\frac{2}{\sqrt{\pi}})^2=\pi\times \frac{4}{\pi}\Rightarrow Area=4$

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All Common Core: 7th Grade Math Resources

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Common Core: 7th Grade Math : Grade 7

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

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #1 : How To Find The Volume Of A Cube

Example Question #1 : Finding Volume Of A Cube

Example Question #931 : Grade 7

Example Question #1 : Finding Volume Of A Cube

Example Question #3 : Finding Volume Of A Cube

Example Question #1 : Area 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 #171 : Plane Geometry

Example Question #11 : Area And Circumference Of A Circle

Example Question #3 : How To Find The Area Of A Circle

All Common Core: 7th Grade Math Resources

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