How to find the volume of a cone in pre-algebra

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Math › How to find the volume of a cone in pre-algebra

Questions 1 - 5

1

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

$18\pi \ m^3$

$54\pi \ m^3$

$72\pi \ m^3$

$9\pi \ m^3$

$36\pi \ m^3$

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:

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

2

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

$384\pi$

$1152\pi$

Explanation

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

We must first solve for the area of the circle using

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 to get

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

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

3

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

$100\pi$

$60\pi$

$30\pi$

$150\pi$

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

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

$Volume=150\pi$ .

4

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

$448\pi$

$168\pi$

$360\pi$

Explanation

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

We must first solve for the area of the circle using

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 to get

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

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

5

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

$100\pi$

$60\pi$

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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