Volume and Surface Area of a Cylinder
For a cylinder with radius
r and height
h:
example
A cylinder has height
5 centimeters and radius
3 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. |
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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 3.14 for π ) |
V=πr2h
V≈(3.14)(3cm)2⋅5cm |
Step 5. Solve. |
V≈141.3cm3 |
Step 6. Check: We leave it to you to check your calculations. |
|
Step 7. Answer the question. |
The volume is approximately 141.3 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 3.14 for π ) |
S=2πr2+2πrh
S≈2(3.14)(3cm)2+2(3.14)(3cm)5cm |
Step 5. Solve. |
S≈150.72cm2 |
Step 6. Check: We leave it to you to check your calculations. |
|
Step 7. Answer the question. |
The surface area is approximately 150.72 square centimeters. |
example
Find 1. the volume and 2. the surface area of a can of soda. The radius of the base is
4 centimeters and the height is
13 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. |
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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 3.14 for π ) |
V=πr2h
V≈(3.14)(4cm)2⋅13cm |
Step 5. Solve. |
V≈653.12cm3 |
Step 6. Check: We leave it to you to check. |
|
Step 7. Answer the question. |
The volume is approximately 653.12 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 3.14 for π ) |
S=2πr2+2πrh
S≈2(3.14)(4cm)2+2(3.14)(4cm)13cm |
Step 5. Solve. |
S≈427.04cm2 |
Step 6. Check: We leave it to you to check your calculations. |
|
Step 7. Answer the question. |
The surface area is approximately 427.04 square centimeters. |
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