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Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

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Example Questions

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

Find the volume, in cubic inches, of a cylinder that has a radius of inches and a height of inches.

Possible Answers:

4456.1 in^3

3308.1 in^3

737.5 in^3

2695.3 in^3

Correct answer:

3308.1 in^3

Explanation:

The formula to find the volume of a cylinder is $\pi r^2\times height$ .

Now, plug in the given numbers into this equation.

$\text{Volume}=\pi \times 9^2 \times 13$

$\text{Volume}=\pi \times 1053=3308.1$ in^3

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Example Question #731 : Geometry

Find the volume of the cylinder if the circular base has an area of $\pi$ , and the height of the cylinder is also $\pi$ .

Possible Answers:

$\frac{\pi^3}{4}$

$\frac{\pi^3}{2}$

$\pi^3$

$\frac{\pi^2}{2}$

$\pi^2$

Correct answer:

$\pi^2$

Explanation:

Write the formula for volume of a cylinder.

$V=\pi r^2 h$

Remember that area of a circle is $A=\pi r^2$

Since the area of the circle is known, substitute the area into the formula.

$V=\pi(\pi)= \pi^2$

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Example Question #491 : Grade 8

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

Possible Answers:

$12.4 \;\textrm{yd}$

$6.2 \;\textrm{yd}$

$15.4 \;\textrm{yd}$

$9.3 \;\textrm{yd}$

$7.7 \;\textrm{yd}$

Correct answer:

$12.4 \;\textrm{yd}$

Explanation:

The volume of a sphere, given its radius, is

$V = \frac{4\pi r^{3}}{3}$

Set V = 1,000 , solve for , and double that to get the diameter.

$1,000= \frac{4\pi r^{3}}{3}$

$r^{3} = \frac{1,000 \cdot 3 }{4\pi} \approx 238.7$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

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Example Question #492 : Grade 8

The diameter of a sphere is . Give the volume of the sphere in terms of .

Possible Answers:

$10\pi t^3$

$72\pi t^3$

$24\pi t^3$

$36\pi t^3$

$30\pi t^3$

Correct answer:

$36\pi t^3$

Explanation:

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times (3t)^3=\frac{4}{3}\pi\times 27t^3\Rightarrow Volume=36\pi t^3$

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Example Question #493 : Grade 8

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

Possible Answers:

723.3m^3

1000m^3

1023.3m^3

523.6m^3

500m^3

Correct answer:

523.6m^3

Explanation:

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}\pi r^3$

where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be $10\div 2=5$ meters. Now we can get:

$Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi\times 5^3=\frac{4}{3}\times \pi \times 125\approx 523.6 m^3$

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Example Question #3 : Volume Of A Three Dimensional Figure

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

Possible Answers:

$12\ inches$

$10\ inches$

$16.4\ inches$

$12.4\ inches$

$10.4\ inches$

Correct answer:

$12.4\ inches$

Explanation:

The volume of a sphere is:

$Volume=\frac{4}{3}\pi r^3$

Where is the radius of the sphere. We know the volume and can solve the formula for :

$Volume=\frac{4}{3}\pi r^3=1000\Rightarrow r^3=\frac{3\times1000 }{4\pi}\approx 238.85\Rightarrow r\approx 6.2$ inches

So we can get:

$Diameter=2r=2\times 6.2=12.4inches$

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Example Question #621 : Geometry

A sphere has a diameter of inches. What is the volume of this sphere?

Possible Answers:

523.6 in^3

458.3 in^3

104.7 in^3

632.9 in^3

Correct answer:

523.6 in^3

Explanation:

To find the volume of a sphere, use the following formula:

$\text{Volume}=\frac{4}{3}\pi\times r^3$ , where is the radius of the sphere.

Now, because we are given the diameter of the sphere, divide that value in half to find the radius.

$r=10\div2=5$

Now, plug this value into the volume equation.

$\text{Volume}=\frac{4}{3}\pi\times 5^3$

$\text{Volume}=\frac{4}{3}\pi\times 125$

$\text{Volume}=\frac{500}{3}\pi=523.6$ in^3

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

What is the volume of a sphere with a diameter of ?

Possible Answers:

$\frac{500}{3}\pi$

$150\pi$

$100\pi$

$200\pi$

$\frac{100}{3}\pi$

Correct answer:

$\frac{500}{3}\pi$

Explanation:

Write the formula for the volume of the sphere.

$V=\frac{4}{3}\pi r^3$

The radius is half the diameter, which is five. Substitute the value.

$V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (5)^3=\frac{4}{3}\pi (125)= \frac{500}{3}\pi$

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Example Question #494 : Grade 8

A cone has height 18 inches; its base has radius 4 inches. Give its volume in cubic feet (leave in terms of $\pi$ )

Possible Answers:

$\frac{1}{18} \pi \textrm{ ft}^{3}$

$\frac{1}{6} \pi \textrm{ ft}^{3}$

$\frac{1}{12} \pi \textrm{ ft}^{3}$

$\frac{1}{4} \pi \textrm{ ft}^{3}$

$\frac{1}{3} \pi \textrm{ ft}^{3}$

Correct answer:

$\frac{1}{18} \pi \textrm{ ft}^{3}$

Explanation:

Convert radius and height from inches to feet by dividing by 12:

Height: 18 inches = $18 \div 12 = \frac{18}{12} = \frac{3}{2}$ feet

Radius: 4 inches = $4 \div 12 = \frac{4}{12} = \frac{1}{3}$

The volume of a cone is given by the formula

$V = \frac{1}{3} \pi r^{2} h$

Substitute $r = \frac{1}{3}, h = \frac{3}{2}$ :

$V = \frac{1}{3}\cdot \left ( \frac{1}{3} \right ) ^{2}\cdot \frac{3}{2} \cdot \pi$

$V = \frac{1}{3}\cdot\frac{1}{3}\cdot \frac{1}{3}\cdot \frac{3}{2} \cdot \pi$

$V = \frac{1}{1}\cdot\frac{1}{3}\cdot \frac{1}{3}\cdot \frac{1}{2} \cdot \pi$

$V = \frac{1}{18} \pi$

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Example Question #495 : Grade 8

A cone has height 240 centimeters; its base has radius 80 centimeters. Give its volume in cubic meters.

Possible Answers:

$0.768 \pi \textrm{ m}^{3}$

$0.512 \pi \textrm{ m}^{3}$

$1.536 \pi \textrm{ m}^{3}$

$4.608 \pi \textrm{ m}^{3}$

Correct answer:

$0.512 \pi \textrm{ m}^{3}$

Explanation:

Convert both dimensions from centimeters to meters by dividing by 100:

Height: 240 centimeters = $240 \div 100 = 2.4$ meters.

Radius: 80 centimeters = $80 \div 100 = 0.8$ meters.

Substitute r = 0.8, h = 2.4 in the volume formula:

$V = \frac{1}{3} \pi r^{2}h$

$V = \frac{1}{3} \cdot \pi \cdot 0.8 ^{2} \cdot 2.4$

$V = \frac{1}{3}\cdot 0.8 \cdot 0.8 \cdot 2.4 \cdot \pi$

$V =0.512 \pi$

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Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

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

Example Question #731 : Geometry

Example Question #491 : Grade 8

Example Question #492 : Grade 8

Example Question #493 : Grade 8

Example Question #3 : Volume Of A Three Dimensional Figure

Example Question #621 : Geometry

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

Example Question #494 : Grade 8

Example Question #495 : Grade 8

All Common Core: 8th Grade Math Resources

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