### All High School Math Resources

## Example Questions

### Example Question #1 : Cylinders

What is the volume of a cylinder with a radius of 2 and a length that is three times as long as its diameter?

**Possible Answers:**

**Correct answer:**

The volume of a cylinder is the base multiplied by the height or length. The base is the area of a circle, which is . Here, the radius is 2. The diameter is 4. Three times the diameter is 12. The height or length is 12. So, the answer is .

### Example Question #1 : Cylinders

A water glass has the shape of a right cylinder. The glass has an interior radius of 2 inches, and a height of 6 inches. The glass is 75% full. What is the volume of the water in the glass (in cubic inches)?

**Possible Answers:**

**Correct answer:**

The volume of a right cylinder with radius and height is:

Since the glass is only 75% full, only 75% of the interior volume of the glass is occupied by water. Therefore the volume of the water is:

### Example Question #1 : How To Find The Volume Of A Cylinder

A circle has a circumference of and it is used as the base of a cylinder. The cylinder has a surface area of . Find the volume of the cylinder.

**Possible Answers:**

**Correct answer:**

Using the circumference, we can find the radius of the circle. The equation for the circumference is ; therefore, the radius is 2.

Now we can find the area of the circle using . The area is .

Finally, the surface area consists of the area of two circles and the area of the mid-section of the cylinder: , where is the height of the cylinder.

Thus, and the volume of the cylinder is .

### Example Question #1 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder that has a base with a radius of 5 and a height of 52?

**Possible Answers:**

**Correct 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 height is 52 and the radius is 5 which we plug into our equation which will look like this

We then square the 5 to get

Then perform multiplication to get

### Example Question #11 : Cylinders

What is the surface area of a cylinder with a radius of 2 cm and a height of 10 cm?

**Possible Answers:**

40π cm^{2 }

56π cm^{2 }

48π cm^{2 }

32π cm^{2 }

36π cm^{2 }

**Correct answer:**

48π cm^{2 }

SA_{cylinder} = 2πrh + 2πr^{2} = 2π(2)(10) + 2π(2)^{2} = 40π + 8π = 48π cm^{2}

### Example Question #4 : How To Find The Volume Of A Cylinder

A cylinder has a radius of and a height of . What is its volume?

**Possible Answers:**

**Correct answer:**

In order to calculate the volume of a cylinder, we must utilize the formula . We were given the radius, , and the height, .

Insert the known variables into the formula and solve for volume .

In essence, we find the area of the cylinder's circular base, , and multiply it by the height.

### Example Question #1 : How To Find The Volume Of A Cylinder

A cylinder has a radius of and a height of . What is its volume

**Possible Answers:**

Not enough information to solve.

**Correct answer:**

In order to calculate the volume of a cylinder, we must utilize the formula . We were given the radius, , and the height, .

Insert the known variables into the formula and solve for volume .

In essence, we find the area of the cylinder's circular base, , and multiply it by the height.

### Example Question #1 : How To Find The Volume Of A Cylinder

A sphere with a radius of is circumscribed in a cylinder. What is the cylinder's volume?

**Possible Answers:**

Not enough information to solve

**Correct answer:**

In order to solve this problem, one key fact needs to be understood. A sphere will take up exactly of the volume of a cylinder in which it is circumscribed. Therefore, if we find the volume of the sphere we can then solve for the volume of the cylinder.

First, we need to find the volume of the sphere.

This equals of the volume of the cylinder. Therefore,

### Example Question #1 : How To Find The Volume Of A Cylinder

Calculate the volume of a cylinder with a height of six, and a base with a radius of three.

**Possible Answers:**

**Correct answer:**

The volume of a cylinder is give by the equation .

In this example, and .

### Example Question #8 : How To Find The Volume Of A Cylinder

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

**Possible Answers:**

**Correct 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

We then square the to get

Then perform multiplication to get

The answer is .