### All ACT Math Resources

## Example Questions

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

A certain cylinder has diameter that is twice the length of its height. If the volume of the cylinder is cubic inches, what is its radius?

**Possible Answers:**

**Correct answer:**

The volume of a cylinder is:

You can think of the volume as the area of the base times the height. Since it is given that the diameter is twice the length of the height, the radius (half the diameter) equals the height. If it helps to visualize these dimensions, draw the cylinder described.

The equation can be rewritten, using the height in terms of the radius.

Plug in the given volume to solve for the radius.

### Example Question #2 : How To Find The Volume Of A Cylinder

The radius of a cylinder is five and its height is nine. What is its volume?

**Possible Answers:**

**Correct answer:**

To solve this question, you must remember that the formula for volume is the product of the area of the base and the height. The area of the base of this cylinder is .

Plug in the given radius and height to solve.

### Example Question #3 : How To Find The Volume Of A Cylinder

What is the volume of a round metal washer with an outer radius of 8 in, an inner radius of 2 in, and a thickness of 0.5 in?

**Possible Answers:**

**Correct answer:**

The volume of a cylinder is given by the formula: .

For a shape with a hole through the center, the final volume is equal to the total volume of the shape minus the volume of the inner hole. In this question, we are looking for the volume given by the larger radius minus the volume given by the smaller radius. The height is equal to the thickness of the washer.

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

How much more volume can a cylinder hold than a cone given that both have the same radius and height?

Here B represents the area of the Base, and h the height.

**Possible Answers:**

None of the answers are correct

**Correct answer:**

Cylinder: Cone:

Thus the difference is 2/3Bh and that means a cylinder can hold 2/3Bh more given the same radius and height.

### Example Question #5 : How To Find The Volume Of A Cylinder

The height of a right circular cylinder is and its radius is . What is the volume, in cubic meters, of the cylinder?

**Possible Answers:**

**Correct answer:**

The volume of a right circular cylinder is equal to its height () multiplied by the area of the circle base ().

In this scenario, the Volume

.

Therefore, the volume is .

### Example Question #6 : How To Find The Volume Of A Cylinder

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

**Possible Answers:**

**Correct answer:**

Plug the radius and height into the formula for the volume of a cylinder:

### Example Question #7 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder with a base diameter of 12 and a height of 3? Leave your answer in terms of

**Possible Answers:**

**Correct answer:**

To find the volume of a cylinder use formula:

For a cylinder with a radius of 6 and a height of 3 this yields:

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

A cylindrical drum is being constructed as part of a water purifying plant. Contaminated water will flow into the top half of the drum and be forced by pressure through a mesh filter into the lower half of the drum, where the clean water will then exit through a funnel. The drum's filter must be replaced when the total sediment content exceeds of the drum's volume.

If the drum is feet tall and feet in diameter, how many cubic feet of sediment can the drum hold before the filter must be changed? Round your final answer to the nearest integer.

**Possible Answers:**

**Correct answer:**

The formula for volume of a cylinder is , where is the height of the cylinder.

Since our diameter is feet, feet, and feet

Plug in known values and solve.

Since we can only take of our volume as the answer, our answer is

### Example Question #9 : How To Find The Volume Of A Cylinder

Find the volume of a cylinder whose diameter is and height is .

**Possible Answers:**

**Correct answer:**

To find volume, simply use the following formula. Remember, you were given diameter so radius is half of that. Thus,

### Example Question #10 : How To Find The Volume Of A Cylinder

Find the volume of cylinder with diameter of and height of .

**Possible Answers:**

**Correct answer:**

To find volume of a cylinder, simply use the following formula. Thus,

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