How to find the volume of a cylinder - SSAT Upper Level Quantitative

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The height of a cylinder is 3 inches and the radius of the circular end of the cylinder is 3 inches. Give the volume and surface area of the cylinder.

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The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height or:

$Volume=\pi $r^2h$$

where is the radius of the circular end of the cylinder and is the height of the cylinder. So we can write:

$Volume=\pi $r^2h$=\pi \times $3^2$\times $3=84.82in^3$$

The surface area of the cylinder is given by:

$A=2\pi $r^2$+2\pi rh$

where is the surface area of the cylinder, is the radius of the cylinder and is the height of the cylinder. So we can write:

$A=2\pi $r^2$+2\pi rh$

$A=2\pi $(3)^2$+2\pi \times 3\times 3$

$A=18\pi+18\pi$

$A=36\pi$

The height of a cylinder is two times the length of the radius of the circular end of a cylinder. If the volume of the cylinder is $16\pi$ , what is the height of the cylinder?

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The volume of a cylinder is:

$Volume=\pi $r^2h$$

where is the radius of the circular end of the cylinder and is the height of the cylinder.

Since , we can substitute that into the volume formula. So we can write:

$Volume=\pi $r^2h$$

$16\pi=\pi $r^2$\cdot (2r)$

$16\pi =2\pi $r^{3}$$

So we get:

$h=2r=2\times 2=4$

The end (base) of a cylinder has an area of $16\pi$ square inches. If the height of the cylinder is half of the radius of the base of the cylinder, give the volume of the cylinder.

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The area of the end (base) of a cylinder is $\pi $r^2$$ , so we can write:

$\pi $r^2$=16\pi\Rightarrow $r^2$=16\Rightarrow r=4\ inches$

The height of the cylinder is half of the radius of the base of the cylinder, that means:

$h=\frac{r}{2}$=\frac{4}{2}$=2\ inches$

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height:

$Volume=Area\times h=16\pi\times 2=32\pi$

or

$Volume=\pi $r^2h$=\pi\times $4^2$\times 2=32\pi$

We have two right cylinders. The radius of the base Cylinder 1 is $\sqrt{3}$ times more than that of Cylinder 2, and the height of Cylinder 2 is 4 times more than the height of Cylinder 1. The volume of Cylinder 1 is what fraction of the volume of Cylinder 2?

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The volume of a cylinder is:

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

where is the volume of the cylinder, is the radius of the circular end of the cylinder, and is the height of the cylinder.

So we can write:

and

Now we can summarize the given information:

Now substitute them in the formula:

Two right cylinders have the same height. The radius of the base of the first cylinder is two times more than that of the second cylinder. Compare the volume of the two cylinders.

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The volume of a cylinder is:

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

where is the radius of the circular end of the cylinder and is the height of the cylinder. So we can write:

We know that

and

.

So we can write:

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

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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}$=\pi \times 1053=3308.1$

A cylinder has a diameter of inches and a height of inches. Find the volume, in cubic inches, of this cylinder.

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$\text{Volume of cylinder}$=\pi \times $$\text{radius}$^2$ \times $\text{height}$

Since we are given the diameter, divide that value in half to find the radius.

$$\text{radius}$=8\div2=4$

Now plug this value into the equation for the volume of a cylinder.

$$\text{Volume}$=\pi \times $4^4$ \times 2$

$$\text{Volume}$=\pi \times 32=100.5$

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

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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$$

The height of a cylinder is 3 inches and the radius of the circular end of the cylinder is 3 inches. Give the volume and surface area of the cylinder.

Tap to see back →

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height or:

$Volume=\pi $r^2h$$

where is the radius of the circular end of the cylinder and is the height of the cylinder. So we can write:

$Volume=\pi $r^2h$=\pi \times $3^2$\times $3=84.82in^3$$

The surface area of the cylinder is given by:

$A=2\pi $r^2$+2\pi rh$

where is the surface area of the cylinder, is the radius of the cylinder and is the height of the cylinder. So we can write:

$A=2\pi $r^2$+2\pi rh$

$A=2\pi $(3)^2$+2\pi \times 3\times 3$

$A=18\pi+18\pi$

$A=36\pi$

The height of a cylinder is two times the length of the radius of the circular end of a cylinder. If the volume of the cylinder is $16\pi$ , what is the height of the cylinder?

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The volume of a cylinder is:

$Volume=\pi $r^2h$$

where is the radius of the circular end of the cylinder and is the height of the cylinder.

Since , we can substitute that into the volume formula. So we can write:

$Volume=\pi $r^2h$$

$16\pi=\pi $r^2$\cdot (2r)$

$16\pi =2\pi $r^{3}$$

So we get:

$h=2r=2\times 2=4$

The end (base) of a cylinder has an area of $16\pi$ square inches. If the height of the cylinder is half of the radius of the base of the cylinder, give the volume of the cylinder.

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The area of the end (base) of a cylinder is $\pi $r^2$$ , so we can write:

$\pi $r^2$=16\pi\Rightarrow $r^2$=16\Rightarrow r=4\ inches$

The height of the cylinder is half of the radius of the base of the cylinder, that means:

$h=\frac{r}{2}$=\frac{4}{2}$=2\ inches$

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height:

$Volume=Area\times h=16\pi\times 2=32\pi$

or

$Volume=\pi $r^2h$=\pi\times $4^2$\times 2=32\pi$

We have two right cylinders. The radius of the base Cylinder 1 is $\sqrt{3}$ times more than that of Cylinder 2, and the height of Cylinder 2 is 4 times more than the height of Cylinder 1. The volume of Cylinder 1 is what fraction of the volume of Cylinder 2?

Tap to see back →

The volume of a cylinder is:

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

where is the volume of the cylinder, is the radius of the circular end of the cylinder, and is the height of the cylinder.

So we can write:

and

Now we can summarize the given information:

Now substitute them in the formula:

Two right cylinders have the same height. The radius of the base of the first cylinder is two times more than that of the second cylinder. Compare the volume of the two cylinders.

Tap to see back →

The volume of a cylinder is:

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

where is the radius of the circular end of the cylinder and is the height of the cylinder. So we can write:

We know that

and

.

So we can write:

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

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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}$=\pi \times 1053=3308.1$

A cylinder has a diameter of inches and a height of inches. Find the volume, in cubic inches, of this cylinder.

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$\text{Volume of cylinder}$=\pi \times $$\text{radius}$^2$ \times $\text{height}$

Since we are given the diameter, divide that value in half to find the radius.

$$\text{radius}$=8\div2=4$

Now plug this value into the equation for the volume of a cylinder.

$$\text{Volume}$=\pi \times $4^4$ \times 2$

$$\text{Volume}$=\pi \times 32=100.5$

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

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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$$

The height of a cylinder is 3 inches and the radius of the circular end of the cylinder is 3 inches. Give the volume and surface area of the cylinder.

Tap to see back →

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height or:

$Volume=\pi $r^2h$$

where is the radius of the circular end of the cylinder and is the height of the cylinder. So we can write:

$Volume=\pi $r^2h$=\pi \times $3^2$\times $3=84.82in^3$$

The surface area of the cylinder is given by:

$A=2\pi $r^2$+2\pi rh$

where is the surface area of the cylinder, is the radius of the cylinder and is the height of the cylinder. So we can write:

$A=2\pi $r^2$+2\pi rh$

$A=2\pi $(3)^2$+2\pi \times 3\times 3$

$A=18\pi+18\pi$

$A=36\pi$

The height of a cylinder is two times the length of the radius of the circular end of a cylinder. If the volume of the cylinder is $16\pi$ , what is the height of the cylinder?

Tap to see back →

The volume of a cylinder is:

$Volume=\pi $r^2h$$

where is the radius of the circular end of the cylinder and is the height of the cylinder.

Since , we can substitute that into the volume formula. So we can write:

$Volume=\pi $r^2h$$

$16\pi=\pi $r^2$\cdot (2r)$

$16\pi =2\pi $r^{3}$$

So we get:

$h=2r=2\times 2=4$

The end (base) of a cylinder has an area of $16\pi$ square inches. If the height of the cylinder is half of the radius of the base of the cylinder, give the volume of the cylinder.

Tap to see back →

The area of the end (base) of a cylinder is $\pi $r^2$$ , so we can write:

$\pi $r^2$=16\pi\Rightarrow $r^2$=16\Rightarrow r=4\ inches$

The height of the cylinder is half of the radius of the base of the cylinder, that means:

$h=\frac{r}{2}$=\frac{4}{2}$=2\ inches$

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height:

$Volume=Area\times h=16\pi\times 2=32\pi$

or

$Volume=\pi $r^2h$=\pi\times $4^2$\times 2=32\pi$

We have two right cylinders. The radius of the base Cylinder 1 is $\sqrt{3}$ times more than that of Cylinder 2, and the height of Cylinder 2 is 4 times more than the height of Cylinder 1. The volume of Cylinder 1 is what fraction of the volume of Cylinder 2?

Tap to see back →

The volume of a cylinder is:

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

where is the volume of the cylinder, is the radius of the circular end of the cylinder, and is the height of the cylinder.

So we can write:

and

Now we can summarize the given information:

Now substitute them in the formula: