Volume of Cylinders

Volume of Cylinders

Locate your geometry notes. They should already have circle notes completed.

​Add the following notes to your paper. Leave the blank areas open for more information.

Pause and think. What are cubic units?

Since volume is 3-dimensional, we measure it in unit cubes.

• If a shape is measured in inches, the units for volume are cubic inches (inches³)

• If a shape is measured in feet, the units for volume are cubic feet (feet³)

• If a shape is measured in cm, the units for volume are cubic inches (inches³)

​Add the blue notes for the volume formula to your paper

​Pause and Think about the highlighted portion below:

• We need two parts to find the volume:

  • (area of the base) and (height of the cylinder)

• The base is a circle. Do you remember the formula for area of a circle?

  • (A=πr²)

• Keep in mind that r² is the radius times itself, which is where r ⋅ r comes from.

​Let's check out this highlighted portion.

• Height ("h") refers to the height of the cylinder

  • Height will always be the distance between the two bases.

  • In a cylinder, it is the distance from circle to circle.

• If the cylinder is turned on its side, the height would still be the distance between bases.

​Flip your paper over, let's practice

Do you remember the different between exact and approximate?

Add the following information. Do you understand where all values come from? Pause and think about what you are writing.

​Don't forget units. Diameter is a distance, so plain units. (Just feet)

Now you have the radius AND the diameter. You only need ONE of those to find volume. Can you remember which value we need in the formula?

​Let's start with exact volume.

​Remember, exact means we leave our answer "in terms of pi." We treat the π symbol like a variable.

​Pause and look at what you have here. Does it make sense to you? Do you know where every value comes from and why?

Next is approximate volume.

​Remember, approximate means we use a number for pi. In this class, we will always use 3.14 when estimating or approximating pi.

Do you see a shortcut to get from the exact to the approximate volume? Just multiply 192 by 3.14. Most of the work is already done!

• ​Look at the difference between our exact and approximate answers.

  • We kept our answer in terms of pi for the exact volume and left the π in.

  • We used 3.14 for the approximate volume and the π symbol is not written in the final answer, since we already multiplied by 3.14.

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius

• Diameter

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius

• Diameter

Multiple Choice

Which is the correct description of how to find the volume of a cylinder?

• Find the circumference of the base and multiply it by the height of the cylinder.

• Find the area of the base and multiply it by the height of the cylinder.

• Square the area of the base and multiply it by the height of the cylinder

• Find the area of the base and add it to the height of the cylinder.

Multiple Choice

Eric needs to find the area of the base of a cylinder. Which formula will help him?

• $$2\pi r$$

• $$2\pi rh$$

• $$\pi r^2$$

• $$\frac{1}{2\ }bh$$

​Moving forward, there are TWO things you must check for EVERY problem.

• ​#1: Is it looking for the exact or the approximate answer?

  • With exact, leave your answer in terms of pi. (π symbol in answer)

  • With approximate, use 3.14 for pi.

• #2: Were you given the radius or the diameter?

  • You MUST have the radius to find the volume.

  • If given the diameter, divide it by 2 to get the radius.

Multiple Choice

Choir is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches. 

Which equation can be used to find the exact volume of the container?

• V = π(9)

• V = π(4.5)²(32)

• V = π(9)²(32)

• V = π(4.5)(32)

Multiple Choice

What is the volume of the cylinder expressed in terms of pi?

$$V=\pi r^2h$$  

• $$40\pi\ mm^3$$

• $$80\pi\ mm^3$$

• $$320\pi\ mm^3$$

• $$200\pi\ mm^3$$

Multiple Choice

Find the approximate volume of the cylinder using 3.14 for pi. Round your answer to the nearest tenth

• 282.6 in³

• 94.2 in³

• 235.5 in³

• 78.5 in³

Multiple Choice

What is the volume of the cylinder? Express the approximate answer rounded to the nearest whole number.

• 4974 km³

• 1584 km³

• 6336 km³

• 829 km³

Multiple Choice

Jason is burying a drainage pipe that has a radius of 5 in and a height of 43 in. How much water can the drainage pipe hold? Leave the answer in terms of π.

• 1075π in³

• 268.75π in³

• 430π in³

• 806.25π in³

Multiple Choice

Find the volume of the cylinder using 3.14 for pi. Round your answer to the nearest tenth

• 2001.8 mm³

• 400.6 mm³

• 637.5 mm³

• 127.5 mm³

Multiple Choice

Find the approximate volume of the cylinder using 3.14 for pi. Round your answer to the nearest tenth

• 64 cm³

• 201.1 cm³

• 401.9 cm³

• 100.5 cm³

Multiple Choice

What is the volume of the cylinder? Express your exact answer in terms of π.

• 769.7 m³

• 980π m³

• 70π m³

• 245π m³