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High School Math : How to find the volume of a cone in pre-algebra

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Example Questions

Example Question #1 : How To Find The Volume Of A Cone In Pre Algebra

What is the volume of a cone with a base radius of and a height of ?

Possible Answers:

$100\pi$

100

$60\pi$

Correct answer:

$100\pi$

Explanation:

To find the volume of a cone we must use the equation

$Volume\ of\ \ cone=\frac{1}{3}\cdot (area\ of\ base)\cdot (height)$

We must first solve for the area of the base using .

The equation for the area of a circle is

We plug in and square it to get

We then plug our answer into the equation for the cone with to get

We multiply to get our final answer for the volume of the cone .

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Example Question #2 : How To Find The Volume Of A Cone In Pre Algebra

What is the volume of a cone with a circle radius of and a height of ?

Possible Answers:

$168\pi$

168

$360\pi$

$448\pi$

Correct answer:

$448\pi$

Explanation:

To find the volume of a cone we must use the equation

We must first solve for the area of the circle using r=8

The equation for the area of a circle is

We plug in and square it to get

$Area=\pi(64)$

We then plug our answer into the equation for the cone with h=21 to get

$Volume=(\frac{1}{3})(64\pi)(21)$

We multiply to get our final answer for the volume of the cone $448\pi$ .

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Example Question #3 : How To Find The Volume Of A Cone In Pre Algebra

What is the volume of a cone with a circle radius of and a height of ?

Possible Answers:

1152

$1152\pi$

$384\pi$

384

Correct answer:

$384\pi$

Explanation:

To find the volume of a cone we must use the equation

We must first solve for the area of the circle using r=8

The equation for the area of a circle is

We plug in and square it to get $Area=64\pi$

We then plug our answer into the equation for the cone with h=18 to get

$V=(\frac{1}{3})(64\pi)(18)$

We multiply to get our final answer for the volume of the cone $384\pi$ .

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Example Question #161 : Geometry

What is the volume of a cone with a radius of and a height of ?

Possible Answers:

$30\pi$

$100\pi$

$150\pi$

$60\pi$

Correct answer:

$150\pi$

Explanation:

To find the volume of a cone, use the equation:

$Volume=\frac{1}{3}(Area\ of\ Circle)(Height)$

Solve for the area of a circle with radius :

$Area\ of\ Circle=\pi(5^{2})$

$Area\ of\ Circle = 25\pi$

Substitute $25\pi$ for area of circle and for height into the equation for volume

$Volume=\frac{1}{2}(25\pi)(12)$

$Volume=150\pi$ .

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Example Question #162 : Geometry

What is the volume of a cone with a height of meters and a base diameter of meters?

Possible Answers:

$18\pi \ m^3$

$72\pi \ m^3$

$9\pi \ m^3$

$36\pi \ m^3$

$54\pi \ m^3$

Correct answer:

$18\pi \ m^3$

Explanation:

The formula for the volume of a cone is $\frac{1}{3}{\pi}r^{2}h$ .

Notice that we are given the diameter, meters, not the radius; thus, we have to solve for the radius by dividing the diameter by two. The radius is therefore 3 meters. Then, we plug this value into the formula for volume:

$\frac{1}{3}{\pi}(3)^{2}\cdot 6 = \frac{1}{3}{\pi}9\cdot 6 = 18{\pi}\ \textup{meters}^3=18\pi m^3$

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High School Math : How to find the volume of a cone in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find The Volume Of A Cone In Pre Algebra

Example Question #2 : How To Find The Volume Of A Cone In Pre Algebra

Example Question #3 : How To Find The Volume Of A Cone In Pre Algebra

Example Question #161 : Geometry

Example Question #162 : Geometry

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