The axle for a toy car has a length of 4 inches and a diameter of a quarter inch. What is the volume of the axle? Assume it is a cylinder.

Use the following formula for volume of a cylinder

\(\displaystyle V_{cylinder}=\pi r^2h\)

Where r and h are our radius and height, respectively.

In this case, we first need to change our diameter to radius. Because our diameter is one quarter of an inch, our radius will be one eighth of an inch.

Plug it in to get:

\(\displaystyle V_{cylinder}=\pi (\frac{1}{8})^2*4=\pi*\frac{1}{64}in^2*4in=\frac{4\pi}{64}in^3\)

Simplify to get:

\(\displaystyle \frac{4\pi}{64}in^3=\frac{\pi}{16}in^3\)

You are visiting the drive-through at the bank. You put you money in a cylindrical tube with a height of 8 inches and a radius of 2 inches. What is the volume of the tube?

Begin with the formula for volume of a cylinder:

\(\displaystyle V_{cylinder}=\pi r^2h\)

We have r and h, which are our radius and height, respectively. Plug them in and solve

\(\displaystyle V_{cylinder}=\pi (2in)^2*8in=\pi*32in^2\)

Making our answer:

\(\displaystyle 32\pi in^2\)

To find the volume of a cylinder, we will use the following formula:

\(\displaystyle V = \pi \cdot r^2 \cdot h\)

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 8cm.  We know that the diameter is two times the radius.  Therefore, the radius is 4cm.

We also know the height of the cylinder is 5cm.

Knowing this, we can substitute into the formula.

\(\displaystyle V = \pi \cdot (4\text{cm})^2 \cdot 5\text{cm}\)

\(\displaystyle V = \pi \cdot 16\text{cm}^2 \cdot 5\text{cm}\)

\(\displaystyle V = \pi \cdot 80\text{cm}^3\)

\(\displaystyle V = 80\pi \text{ cm}^3\)

To find the volume of a cylinder, we will use the following formula:

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

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 8in.  We also know the diameter is two times the radius.  Therefore, the radius is 4in. 

We also know the height of the cylinder is 7in.

Knowing all of this, we can substitute into the formula.  We get

\(\displaystyle V = \pi \cdot(4\text{in})^2 \cdot 7\text{in}\)

\(\displaystyle V = \pi \cdot 16\text{in}^2 \cdot 7\text{in}\)

\(\displaystyle V = \pi \cdot 112\text{in}^3\)

\(\displaystyle V = 112\pi \text{ in}^3\)

To find the volume of a cylinder, we will use the following formula:

\(\displaystyle V = \pi \cdot r^2 \cdot h\)

where r is the radius, and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 14in.  We also know the diameter is two times the radius.  Therefore, the radius is 7in. 

We know the height of the cylinder is 12in.

Knowing all of this, we can substitute into the formula.  We get

\(\displaystyle V = \pi \cdot (7\text{in})^2 \cdot 12\text{in}\)

\(\displaystyle V = \pi \cdot 49\text{in}^2 \cdot 12\text{in}\)

\(\displaystyle V = \pi \cdot 588\text{in}^3\)

\(\displaystyle V = 588\pi \text{ in}^3\)

Your family owns a farm with a silo for storing grain. If the silo is 40 feet tall and 15 feet in diameter, what volume of grain can it hold?

Begin with the formula for volume of a cylinder.

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

A cylinder is just a circle with height. 

So, we know the height is 40 ft, but what is r?

If you said 15, you would be on track to get the problem wrong. That is because the diameter is 15 ft, so our radius is only 7.5 ft.

Plug these in to get our answer:

\(\displaystyle V=\pi (7.5ft)^2(40ft)=2250 \pi ft^3\)

Our answer should be

\(\displaystyle 2250 \pi ft^3\)

To find the volume of a cylinder, we will use the following formula:

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

where r is the radius and h is the height of the cylinder.

Now, we know the diameter is 12cm.  We know that the diameter is two times the radius.  Therefore, the radius is 6cm.  

We know the height of the cylinder is 7cm.

We know that \(\displaystyle \pi = 3.14\).

Knowing all of this, we can substitute into the formula.  We get

\(\displaystyle V = 3.14 \cdot (6\text{cm})^2 \cdot 7\text{cm}\)

\(\displaystyle V = 3.14 \cdot 36\text{cm}^2 \cdot 7\text{cm}\)

\(\displaystyle V = 3.14 \cdot 252\text{cm}^3\)

\(\displaystyle V = 791.28\text{cm}^3\)

You have a tennis ball canister which is cylindrical. If the radius of the cylinder is 3.5 cm, and the height is 21 cm, what is the volume of the canister?

Begin with the formula for volume of a cylinder:

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

Where r is our radius and h is our height.

Note that the formula is just the formula for the area of a circle times the height, because a cylinder is really just a circle with height.

Now, plug in what we know and solve for V

\(\displaystyle V=\pi (3.5cm)^2 (21cm)=\pi(12.25cm*21cm)=257.25 \pi cm^3\)

So our answer is:

\(\displaystyle V=257.25 \pi cm^3\)

To find the volume of a cylinder, we will use the following formula:

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

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 16in.  We also know the diameter is two times the radius.  Therefore, the radius is 8in. 

We also know the height of the cylinder is 6in.

Knowing all of this, we can substitute into the formula.  We get

\(\displaystyle V = \pi \cdot(8\text{in})^2 \cdot 6\text{in}\)

\(\displaystyle V = \pi \cdot 64\text{in}^2 \cdot 6\text{in}\)

\(\displaystyle V = \pi \cdot 384\text{in}^3\)

\(\displaystyle V = 384\pi \text{ in}^3\)

To find the volume of a cylinder, we will use the following formula:

\(\displaystyle V = \pi \cdot r^2 \cdot h\)

where r is the radius, and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 10in.  We also know the diameter is two times the radius.  Therefore, the radius is 5in. 

We know the height of the cylinder is 12in.

Knowing all of this, we can substitute into the formula.  We get

\(\displaystyle V = \pi \cdot (5\text{in})^2 \cdot 12\text{in}\)

\(\displaystyle V = \pi \cdot 25\text{in}^2 \cdot 12\text{in}\)

\(\displaystyle V = \pi \cdot 300\text{in}^3\)