Volume and Surface Area of a Cylinder
For a cylinder with radius [latex]r[/latex] and height [latex]h:[/latex]
example
A cylinder has height [latex]5[/latex] centimeters and radius [latex]3[/latex] centimeters. Find 1. the volume and 2. the surface area.
Solution
Step 1. Read the problem. Draw the figure and label
it with the given information. 

1. 

Step 2. Identify what you are looking for. 
The volume of the cylinder 
Step 3. Name. Choose a variable to represent it. 
Let V = volume. 
Step 4. Translate.
Write the appropriate formula.
Substitute. (Use [latex]3.14[/latex] for [latex]\pi [/latex] ) 
[latex]V=\pi {r}^{2}h[/latex]
[latex]V\approx \left(3.14\right)({3}cm)^{2}\cdot 5cm[/latex] 
Step 5. Solve. 
[latex]V\approx 141.3cm^3[/latex] 
Step 6. Check: We leave it to you to check your calculations. 

Step 7. Answer the question. 
The volume is approximately [latex]141.3[/latex] cubic centimeters. 
2. 

Step 2. Identify what you are looking for. 
The surface area of the cylinder 
Step 3. Name. Choose a variable to represent it. 
Let S = surface area. 
Step 4. Translate.
Write the appropriate formula.
Substitute. (Use [latex]3.14[/latex] for [latex]\pi [/latex] ) 
[latex]S=2\pi {r}^{2}+2\pi rh[/latex]
[latex]S\approx 2\left(3.14\right)({3}cm)^{2}+2\left(3.14\right)\left(3cm\right)5cm[/latex] 
Step 5. Solve. 
[latex]S\approx 150.72cm^2[/latex] 
Step 6. Check: We leave it to you to check your calculations. 

Step 7. Answer the question. 
The surface area is approximately [latex]150.72[/latex] square centimeters. 
example
Find 1. the volume and 2. the surface area of a can of soda. The radius of the base is [latex]4[/latex] centimeters and the height is [latex]13[/latex] centimeters. Assume the can is shaped exactly like a cylinder.
Answer:
Solution
Step 1. Read the problem. Draw the figure and
label it with the given information. 

1. 

Step 2. Identify what you are looking for. 
The volume of the cylinder 
Step 3. Name. Choose a variable to represent it. 
Let V = volume. 
Step 4. Translate.
Write the appropriate formula.
Substitute. (Use [latex]3.14[/latex] for [latex]\pi [/latex] ) 
[latex]V=\pi {r}^{2}h[/latex]
[latex]V\approx \left(3.14\right)({4}cm)^{2}\cdot 13cm[/latex] 
Step 5. Solve. 
[latex]V\approx 653.12cm^3[/latex] 
Step 6. Check: We leave it to you to check. 

Step 7. Answer the question. 
The volume is approximately [latex]653.12[/latex] cubic centimeters. 
2. 

Step 2. Identify what you are looking for. 
The surface area of the cylinder 
Step 3. Name. Choose a variable to represent it. 
Let S = surface area. 
Step 4. Translate.
Write the appropriate formula.
Substitute. (Use [latex]3.14[/latex] for [latex]\pi [/latex] ) 
[latex]S=2\pi {r}^{2}+2\pi rh[/latex]
[latex]S\approx 2\left(3.14\right)({4}cm)^{2}+2\left(3.14\right)\left(4cm\right)13cm[/latex] 
Step 5. Solve. 
[latex]S\approx 427.04cm^2[/latex] 
Step 6. Check: We leave it to you to check your calculations. 

Step 7. Answer the question. 
The surface area is approximately [latex]427.04[/latex] square centimeters. 
Did you have an idea for improving this content? We’d love your input.