You are filling a cylindrical hole with concrete, and need to know how much concrete to mix. If the hole is  deep and has a radius of , what volume of concrete will be needed to fill the hole?

Our formula for volume of a cylinder is:

Now, before we start plugging stuff in, we need to have all our measurements be in the same units. Let's switch to feet so that we are consistent.

Now, let's plug it in and solve:

So, we need 

 of concrete

Recall how to find the volume of a cylinder:

Since Helen is only taking out half the water, we will need to find half the volume of the cylindrical fish tank. Thus, we can write the following equation:

Plug in the given radius and height to find the volume of water that Helen needs to remove.

While exploring the woods near your house, you find a cylindrical hole in the ground. You decide that it is dangerous and should be filled in with concrete so that nobody falls in and hurts themselves. You find that the hole is 20 feet deep and 6 feet wide. How many cubic feet of concrete will you need to fill in the hole?

We need to find the volume of a cylinder. Use the following formula

A cylinder is really just a circle with height.

We know our height, 20ft. 

Our radius is half of the width of the hole. In this case, our width is 6ft, so our radius is 3 ft.

Plug these in and find our volume.

So our answer is:

How much water would be required to fill a tube which is 3 ft wide and 18 ft long?

We are indirectly asked to find the volume of a cylinder. To do so, we need to following formula:

Where r is the radius of our cylinder, and h is the height.

First, we need to change our diameter (3ft) to our radius. The radius is always half the diameter, so our radius is 1.5 ft

Next, plug in our radius and height and solve for V.

So, we have our answer:

Recall how to find the volume of a cylinder:

Plug in the given radius and height to find the volume.

The soft drink can is able to hold a volume of  cubic centimeters of liquid.

The volume of a cylinder can be solved for very simply. Just make sure you have the formula for volume handy! 

The formula for the volume of a cylinder is: , where r is radius and h is the height. It's helpful to remember that volume will provide a value in units cubed, where area or surface area will provide a value in units squared. This minor detail confuses many students. 

Looking at the problem, we have been provided with the height and the diameter. This problem provides a slight curve ball in that we indirectly have been given the radius, so we need to do some detective work. What is the relationship between radius and diameter? The diameter is twice the radius. Or in math speak: . This means we can solve for our radius by taking half of the diameter. Therefore, the radius is  inches. 

Now we are ready to "plug and chug" to get our final answer. 

 cubed inches

The volume of a cylinder can be solved for very simply. Just make sure you have the formula for volume handy! 

The formula for the volume of a cylinder is: , where r is radius and h is the height. It's helpful to remember that volume will provide a value in units cubed, where area or surface area will provide a value in units squared. This minor detail confuses many students. 

Looking at the problem, we have been provided with the height kind of) and the diameter. This problem provides a slight curve ball in that we indirectly have been given the radius and height, so we need to do some detective work. What is the relationship between radius and diameter? The diameter is twice the radius. Or in math speak: . This means we can solve for our radius by taking half of the diameter. Therefore, the radius is . Now we can figure out the value of the height. The problem says it is three times the radius. Therefore, , so the height is 18.

Now we are ready to "plug and chug" to get our final answer. 

 cubed units 

The volume of a cylinder can be solved for very simply. Just make sure you have the formula for volume handy! 

The formula for the volume of a cylinder is: , where r is radius and h is the height. It's helpful to remember that volume will provide a value in units cubed, where area or surface area will provide a value in units squared. This minor detail confuses many students. 

Looking at the problem, we have been provided with the height and the circumference. This problem provides a slight curve ball in that we indirectly have been given the radius, so we need to do some detective work. What is the relationship between radius and circumference?  The circumference is  times the diameter. This can be mathematically defined as: . 

We may solve for the diameter by using this formula. Keep in mind we are solving for d. 

Now divide both sides by  to solve for d. 

We're almost there. Now we need to solve for the radius. The diameter is twice the radius. Or in math speak: . This means we can solve for our radius by taking half of the diameter. Therefore, the radius is .  

Now we are ready to "plug and chug" to get our final answer.