Example 9.56 from Prealgebra, 9.6 Solve Geometry Applications: Volume and Surface Area

Solve Geometry Applications: Volume and Surface Area: example 9.56

Marty’s favorite gastro pub serves french fries in a paper wrap shaped like a cone. What is the volume of a conic wrap that is $8$ inches tall and $5$ inches in diameter? Round the answer to the nearest hundredth.

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.

How many cubic inches of candy will fit in a cone-shaped piñata that is $18$ inches long and $12$ inches across its base? Round the answer to the nearest hundredth.

How did it go?

Step 1. Read the problem. Draw the figure and label it with the given information. Notice here that the base is the circle at the top of the cone.
Step 2. Identify what you are looking for.	the volume of the cone
Step 3. Name. Choose a variable to represent it.	let V = volume
Step 4. Translate. Write the appropriate formula. Substitute. (Use 3.14 for $π$ , and notice that we were given the distance across the circle, which is its diameter. The radius is 2.5 inches.)	$V = \frac{1}{3} π r^{2} h$ $V \approx \frac{1}{3} 3.14 {(2.5)}^{2} (8)$
Step 5. Solve.	$V \approx 52.33$
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question.	The volume of the wrap is approximately 52.33 cubic inches.

Step 1. Read the problem. Draw the figure and label it with the given information. Notice here that the base is the circle at the top of the cone.
Step 2. Identify what you are looking for.	the volume of the cone
Step 3. Name. Choose a variable to represent it.	let V = volume
Step 4. Translate. Write the appropriate formula. Substitute. (Use 3.14 for $π$ , and notice that we were given the distance across the circle, which is its diameter. The radius is 2.5 inches.)	$V = \frac{1}{3} π r^{2} h$ $V \approx \frac{1}{3} 3.14 {(2.5)}^{2} (8)$
Step 5. Solve.	$V \approx 52.33$
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question.	The volume of the wrap is approximately 52.33 cubic inches.

Solve Geometry Applications: Volume and Surface Area: example 9.56

Solution

Your turn

Solve Geometry Applications: Volume and Surface Area: example 9.56

Solution

Your turn