Exemplo 9.52 de Prealgebra, 9.6 Solve Geometry Applications: Volume and Surface Area

Solve Geometry Applications: Volume and Surface Area: exemplo 9.52

Problema e solução em inglês, como no livro original.

A globe of Earth is in the shape of a sphere with radius $14$ centimeters. Find its ⓐ volume and ⓑ surface area. Round the answer to the nearest hundredth.

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A beach ball is in the shape of a sphere with radius of $9$ inches. Find its ⓐ volume and ⓑ surface area.

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ⓐ
Step 2. Identify what you are looking for.	the volume of the sphere
Step 3. Name. Choose a variable to represent it.	let V = volume
Step 4. Translate. Write the appropriate formula. Substitute. (Use 3.14 for $π$ )	$V = \frac{4}{3} π r^{3}$ $V \approx \frac{4}{3} (3.14) 14^{3}$
Step 5. Solve.	$V \approx 11,488.21$
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question.	The volume is approximately 11,488.21 cubic inches.

ⓑ
Step 2. Identify what you are looking for.	the surface area of the sphere
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 $π$ )	$S = 4 π r^{2}$ $S \approx 4 (3.14) 14^{2}$
Step 5. Solve.	$S \approx 2461.76$
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question.	The surface area is approximately 2461.76 square inches.

ⓐ
Step 2. Identify what you are looking for.	the volume of the sphere
Step 3. Name. Choose a variable to represent it.	let V = volume
Step 4. Translate. Write the appropriate formula. Substitute. (Use 3.14 for $π$ )	$V = \frac{4}{3} π r^{3}$ $V \approx \frac{4}{3} (3.14) 14^{3}$
Step 5. Solve.	$V \approx 11,488.21$
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question.	The volume is approximately 11,488.21 cubic inches.

ⓑ
Step 2. Identify what you are looking for.	the surface area of the sphere
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 $π$ )	$S = 4 π r^{2}$ $S \approx 4 (3.14) 14^{2}$
Step 5. Solve.	$S \approx 2461.76$
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question.	The surface area is approximately 2461.76 square inches.

Solve Geometry Applications: Volume and Surface Area: exemplo 9.52

Solução

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Solve Geometry Applications: Volume and Surface Area: exemplo 9.52

Solução

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