Volume of a Figure - High School Math

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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 $448\pi$ .

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Question

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

Answer

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 $384\pi$ .

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Question

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

Answer

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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Question

What is the volume of a cylinder with a circular side with a radius of and a length of ?

Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is

In this example the length is and the radius is so our equation will look like this $Volume=\pi(6^{2})(12)$

We then square the to get .

Then perform multiplication to get $432\pi$ .

The answer is $432\pi$ .

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Question

What is the volume of a cylinder with a circle radius of and a length of ?

Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is .

Here the length is and the radius is , so the equation becomes $V=(8^{2})(14)(\pi)$ .

First square the to get $8^{2}=64$ .

Then perform multiplication to get $(64)(14)(\pi)=896\pi$ .

The answer is therefore $896\pi$ .

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Question

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

Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$

Plug in our given numbers to solve:

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

$V=(\pi 2^2)9$

$V=4\pi9$

$V=36\pi$

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Question

What is the radius of a cylinder with a volume of $144\pi$ and a height of ?

Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$144\pi=(\pi r^2)*9$

Divide both sides by .

$\frac{144\pi}{9}=\pi r^2$

$16\pi=\pi r^2$

Divide both sides by $\pi$ .

Take the square root of both sides:

$\sqrt{16}=\sqrt{r^2}$

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Question

What is the height of a cylinder with a volume of $384\pi$ and a radius of ?

Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$384\pi=(\pi 8^2)h$

$384\pi=64\pih$

Divide both sides by $64\pi$ :

$\frac{384\pi}{64\pi}=h$

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Question

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

Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$V=(\pi 3^2)7$

$V=9\pi7$

$V=63\pi$

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Question

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

Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$V=(\pi 5^2)2$

$V=25\pi2$

$V=50\pi$

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Question

What is the radius of a cylinder with a volume of $128\pi$ and a height of ?

Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$128\pi=(\pi r^2)*8$

Divide both sides by .

$\frac{128\pi}{8}=\pi r^2$

$16\pi=\pi r^2$

Divide both sides by $\pi$ .

Take the square root of both sides:

$\sqrt{16}=\sqrt{r^2}$

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Question

What is the volume of a cylinder with a circle radius of and a length of ?

Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder, which is .

In this example, the length is and the radius is , so our equation will look like this: $V=(8^{2})(21)(\pi)$

We then square the to get $8^{2}=64$ .

Then perform multiplication to get $V=1344\pi$ .

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Question

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

Answer

When thinking about volume, think of it as a stack of something. In this case, a cylinder is a stack of circles. We want the area of the bottom circle times the height, or $V=(\pi r^2)h$ .

Plug in our given information and solve:

$V=(\pi3^2)6$

$V=9\pi6$

$V=54\pi$

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Question

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

Answer

When thinking about volume, think of it as a stack of something. In this case, a cylinder is a stack of circles. We want the area of the bottom circle times the height, or $V=(\pi r^2)h$ .

Plug in and solve:

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

$V=(\pi 4^2)5$

$V=16\pi5$

$V=80\pi$

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Question

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

Answer

When thinking about volume, think of it as a stack of something. In this case, a cylinder is a stack of circles. We want the area of the bottom circle times the height, or $V=(\pi r^2)h$ .

Plug in and solve:

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

$V=(\pi 2^2)10$

$V=4\pi10$

$V=40\pi$

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Question

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

Answer

The formula for the volume of a cylinder is the area of the base circle times the height, or $V=\pi r^2h$ .

Plug in our given info to solve.

$V=\pi r^2h$

$V=\pi 10^210$

$V=100\pi10$

$V=1000\pi$

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Question

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

Answer

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

$A=49\pi$

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

$V=\frac{1}{3}\cdot (49\pi)\cdot (24)$

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

$V=392\pi$

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Question

What is the volume of a cylinder with a circular side with a radius of and a length of ?

Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is

In this example the length is and the radius is so our equation will look like this

$V=7^{2}(\pi)(44)$

We then square the to get

$V=(49)(\pi)(44)$

Then perform multiplication to get $V=2156\pi$ .

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