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. |
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