Solve Geometry Applications: Volume and Surface Area: example 9.53

A cylinder has height $5$ centimeters and radius $3$ centimeters. Find the ⓐ volume and ⓑ surface area.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the ⓐ volume and ⓑ surface area of the cylinder with radius 4 cm and height 7cm.

How did it go?

ⓐ
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 $π$ )	$V = π r^{2} h$ $V \approx (3.14) 3^{2} \cdot 5$
Step 5. Solve.	$V \approx 141.3$
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question.	The volume is approximately 141.3 cubic inches.

ⓑ
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 $π$ )	$S = 2 π r^{2} + 2 π r h$ $S \approx 2 (3.14) 3^{2} + 2 (3.14) (3) 5$
Step 5. Solve.	$S \approx 150.72$
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 inches.

ⓐ
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 $π$ )	$V = π r^{2} h$ $V \approx (3.14) 3^{2} \cdot 5$
Step 5. Solve.	$V \approx 141.3$
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question.	The volume is approximately 141.3 cubic inches.

ⓑ
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 $π$ )	$S = 2 π r^{2} + 2 π r h$ $S \approx 2 (3.14) 3^{2} + 2 (3.14) (3) 5$
Step 5. Solve.	$S \approx 150.72$
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 inches.