**Problem 19: Water Tank Volume Calculation** Sara is moving to Hawaii and will live in the rainforest. She needs a water tank to catch her own water. The cylindrical tank has a diameter of 7.5 feet and a height of 12 feet. **Question:** What is the volume of the tank in cubic feet? Round the answer to the nearest cubic foot. **Solution Overview:** To find the volume of a cylindrical tank, we use the formula for the volume of a cylinder: \[ V = \pi r^2 h \] where: - \( V \) is the volume, - \( r \) is the radius of the base, - \( h \) is the height of the cylinder, - \( \pi \approx 3.14159 \). Here are the steps to calculate the volume: 1. Identify the radius of the cylinder. Since the diameter is given as 7.5 feet, the radius \( r \) is half of the diameter: \[ r = \frac{7.5}{2} = 3.75 \text{ feet} \] 2. Use the height \( h = 12 \text{ feet} \). 3. Substitute the radius and height into the volume formula: \[ V = \pi (3.75)^2 (12) \] 4. Perform the calculations: \[ V \approx 3.14159 \times 14.0625 \times 12 \approx 531.15 \] Rounded to the nearest cubic foot, the volume is approximately 531 cubic feet. **Critical Thinking Section:** Outcome: A critical thinker questions, searches for a deep understanding, evaluates ideas and information, and applies knowledge to solve real-world problems. In this exercise, students apply geometric knowledge to compute the volume of a cylindrical tank, demonstrating the application of mathematical formulas in practical contexts.
**Problem 19: Water Tank Volume Calculation** Sara is moving to Hawaii and will live in the rainforest. She needs a water tank to catch her own water. The cylindrical tank has a diameter of 7.5 feet and a height of 12 feet. **Question:** What is the volume of the tank in cubic feet? Round the answer to the nearest cubic foot. **Solution Overview:** To find the volume of a cylindrical tank, we use the formula for the volume of a cylinder: \[ V = \pi r^2 h \] where: - \( V \) is the volume, - \( r \) is the radius of the base, - \( h \) is the height of the cylinder, - \( \pi \approx 3.14159 \). Here are the steps to calculate the volume: 1. Identify the radius of the cylinder. Since the diameter is given as 7.5 feet, the radius \( r \) is half of the diameter: \[ r = \frac{7.5}{2} = 3.75 \text{ feet} \] 2. Use the height \( h = 12 \text{ feet} \). 3. Substitute the radius and height into the volume formula: \[ V = \pi (3.75)^2 (12) \] 4. Perform the calculations: \[ V \approx 3.14159 \times 14.0625 \times 12 \approx 531.15 \] Rounded to the nearest cubic foot, the volume is approximately 531 cubic feet. **Critical Thinking Section:** Outcome: A critical thinker questions, searches for a deep understanding, evaluates ideas and information, and applies knowledge to solve real-world problems. In this exercise, students apply geometric knowledge to compute the volume of a cylindrical tank, demonstrating the application of mathematical formulas in practical contexts.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**Problem 19: Water Tank Volume Calculation**
Sara is moving to Hawaii and will live in the rainforest. She needs a water tank to catch her own water. The cylindrical tank has a diameter of 7.5 feet and a height of 12 feet.
**Question:**
What is the volume of the tank in cubic feet? Round the answer to the nearest cubic foot.
**Solution Overview:**
To find the volume of a cylindrical tank, we use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \approx 3.14159 \).
Here are the steps to calculate the volume:
1. Identify the radius of the cylinder. Since the diameter is given as 7.5 feet, the radius \( r \) is half of the diameter:
\[ r = \frac{7.5}{2} = 3.75 \text{ feet} \]
2. Use the height \( h = 12 \text{ feet} \).
3. Substitute the radius and height into the volume formula:
\[ V = \pi (3.75)^2 (12) \]
4. Perform the calculations:
\[ V \approx 3.14159 \times 14.0625 \times 12 \approx 531.15 \]
Rounded to the nearest cubic foot, the volume is approximately 531 cubic feet.
**Critical Thinking Section:**
Outcome: A critical thinker questions, searches for a deep understanding, evaluates ideas and information, and applies knowledge to solve real-world problems.
In this exercise, students apply geometric knowledge to compute the volume of a cylindrical tank, demonstrating the application of mathematical formulas in practical contexts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8918ac98-5bcf-465f-8c11-409b4d478a84%2Fac32c637-782e-4768-8c3c-a2eee7b151fb%2Fr2ol17p.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 19: Water Tank Volume Calculation**
Sara is moving to Hawaii and will live in the rainforest. She needs a water tank to catch her own water. The cylindrical tank has a diameter of 7.5 feet and a height of 12 feet.
**Question:**
What is the volume of the tank in cubic feet? Round the answer to the nearest cubic foot.
**Solution Overview:**
To find the volume of a cylindrical tank, we use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \approx 3.14159 \).
Here are the steps to calculate the volume:
1. Identify the radius of the cylinder. Since the diameter is given as 7.5 feet, the radius \( r \) is half of the diameter:
\[ r = \frac{7.5}{2} = 3.75 \text{ feet} \]
2. Use the height \( h = 12 \text{ feet} \).
3. Substitute the radius and height into the volume formula:
\[ V = \pi (3.75)^2 (12) \]
4. Perform the calculations:
\[ V \approx 3.14159 \times 14.0625 \times 12 \approx 531.15 \]
Rounded to the nearest cubic foot, the volume is approximately 531 cubic feet.
**Critical Thinking Section:**
Outcome: A critical thinker questions, searches for a deep understanding, evaluates ideas and information, and applies knowledge to solve real-world problems.
In this exercise, students apply geometric knowledge to compute the volume of a cylindrical tank, demonstrating the application of mathematical formulas in practical contexts.
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