# Cylinders

This page is devoted to learning and investigating the properties and features of Cylinders. Updated June, 2014.

Application Problems created by Ball State students for Area and Volume are linked here:
Campbell's Soup Can
Salt Packing
Water Glasses

Learning Objective: Understand the features of a cylinder
Vocabulary: cylinder, circle, estimation, surface area, volume

• Create a model of a cylinder that has a radius of 3 m and height of 4 m.
• Estimate and then find the surface area with the formula and with SketchUp.
• Estimate and then find the volume with the formula and with SketchUp.

Open Beginning Training Template - Meters

Select Window | Model Info and set the precision to hundredths.

Step 1: Create the base of the cylinder
• Draw a circle in the red-green plane with a radius of 3 meters.
• Confirm your measurement with the text tool.
• Paint the circle yellow.

Step 2: Create a cylinder
• Rotate the circle so you can clearly pull the surface "up" in the direction of the blue axis with the push/pull tool.
• Pull up for a height of 4 meters.
• Paint the lateral surface green.

Step 3: Estimate the Surface Area
• Estimate the area of the top and bottom bases.

• Find the Lateral Surface Area.
• Hint: Sketch the rectangle and mark off three "diameter sections" in meters (think of pealing open the cylinder).
• See Circle Vocabulary for more on how to find the circumference of a circle using a conceptual approach (recall the peace sign).
• Hint: What is the height of this rectangle?
• Estimate the lateral surface area.

• Add the calculations to find the lateral surface area of the cylinder.

Step 4: Find the Surface Area on SketchUp
• Select the yellow circle and use the Entity Information menu to find the area of the base.

• Select the green lateral surface and use the Entity Information menu to find the lateral surface area.
• Note - I was only able to find the lateral surface area on a Mac

Calculate the Area of the Circular Base with the formula (to two decimal places)
A = Pi * radius squared
A = 3.14 * r^2
A = 3.14 * (3 m)^2 = 28.26 m^2
Note that the calculations will not match because a SketchUp circle is actually a 24-gon.

Calculate the Lateral Surface Area with the formula (to two decimal places)
A = circumference * height
A = 3.14 * d * h
A = 3.14 * 6 m * 4 m = 75.36 m2

Total Surface Area = 75.36 m^2 + 28.26 m^2 + 28.26 m^2 = 131.88 m^2
Note that the calculations will not match because a SketchUp circle is actually a 24-gon.

Step 5: Estimate the Volume
• The volume of a right cylinder is calculated in cubic meters.
• Think about the 1 meter layers in this model.
• Use the section tool to illustrate layers.
• Recall that the radius is 3 meters and the height is 4 meters.

Step 6: Create a Group to find the Volume in SketchUp
• Create a new cylinder with the same dimensions.
• Select the entire cylinder.
• Edit > Make Group [Command G] (or right mouse click)
• Use the Entity Information menu to find the Volume.

Calculate the Volume of the Cylinder (to two decimal places)
V = Area of Base * Height
V = 28.26 m^2 * 4 m = 113.04 m^3
Note that the calculations will not match because a SketchUp circle is actually a 24-gon.