What Is The Volume Of A Hemisphere With A Radius Of 4.9 Ft, Rounded To The Nearest Tenth Of A Cubic Foot?Submit Your Answer In Ft³.
Introduction
In mathematics, a hemisphere is half of a sphere. It is a three-dimensional shape that has a curved surface and a flat base. The volume of a hemisphere can be calculated using a specific formula, which involves the radius of the hemisphere. In this article, we will discuss how to calculate the volume of a hemisphere with a given radius and provide a step-by-step solution to the problem.
Understanding the Formula
The formula to calculate the volume of a hemisphere is:
V = (2/3)πr³
Where:
- V is the volume of the hemisphere
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the hemisphere
Given Problem
The problem states that we need to find the volume of a hemisphere with a radius of 4.9 ft, rounded to the nearest tenth of a cubic foot.
Step-by-Step Solution
To solve this problem, we will follow these steps:
- Identify the given values: The radius of the hemisphere is given as 4.9 ft.
- Plug in the values into the formula: We will substitute the given value of the radius into the formula to calculate the volume.
- Calculate the volume: We will perform the necessary calculations to find the volume of the hemisphere.
- Round the answer to the nearest tenth: We will round the calculated volume to the nearest tenth of a cubic foot.
Step 1: Identify the Given Values
The radius of the hemisphere is given as 4.9 ft.
Step 2: Plug in the Values into the Formula
We will substitute the given value of the radius into the formula:
V = (2/3)π(4.9)³
Step 3: Calculate the Volume
To calculate the volume, we will perform the necessary calculations:
V = (2/3) × 3.14159 × (4.9)³ V = (2/3) × 3.14159 × 119.519 V = 2.0944 × 119.519 V = 250.999
Step 4: Round the Answer to the Nearest Tenth
We will round the calculated volume to the nearest tenth of a cubic foot:
V ≈ 251.0 ft³
Conclusion
In this article, we discussed how to calculate the volume of a hemisphere using a specific formula. We provided a step-by-step solution to the problem of finding the volume of a hemisphere with a radius of 4.9 ft, rounded to the nearest tenth of a cubic foot. The calculated volume is approximately 251.0 ft³.
Additional Information
- The formula to calculate the volume of a hemisphere is V = (2/3)πr³.
- The radius of the hemisphere is the distance from the center of the hemisphere to the edge of the hemisphere.
- The volume of a hemisphere is always greater than the volume of a sphere with the same radius.
References
- "Mathematics for Dummies" by Mary Jane Sterling
- "Geometry: A Comprehensive Introduction" by Dan Pedoe
Related Topics
- Calculating the volume of a sphere
- Understanding the formula for the volume of a hemisphere
- Solving problems involving the volume of a hemisphere
Frequently Asked Questions (FAQs) About the Volume of a Hemisphere ====================================================================
Introduction
In our previous article, we discussed how to calculate the volume of a hemisphere using a specific formula. We also provided a step-by-step solution to the problem of finding the volume of a hemisphere with a radius of 4.9 ft, rounded to the nearest tenth of a cubic foot. In this article, we will answer some frequently asked questions (FAQs) about the volume of a hemisphere.
Q: What is the formula for the volume of a hemisphere?
A: The formula for the volume of a hemisphere is V = (2/3)πr³, where V is the volume of the hemisphere, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the hemisphere.
Q: What is the radius of a hemisphere?
A: The radius of a hemisphere is the distance from the center of the hemisphere to the edge of the hemisphere.
Q: How do I calculate the volume of a hemisphere?
A: To calculate the volume of a hemisphere, you need to plug in the value of the radius into the formula V = (2/3)πr³ and perform the necessary calculations.
Q: What is the difference between the volume of a hemisphere and a sphere?
A: The volume of a hemisphere is always greater than the volume of a sphere with the same radius. This is because a hemisphere has a curved surface and a flat base, while a sphere has a curved surface and no flat base.
Q: Can I use the formula for the volume of a sphere to calculate the volume of a hemisphere?
A: No, you cannot use the formula for the volume of a sphere to calculate the volume of a hemisphere. The formula for the volume of a sphere is V = (4/3)πr³, which is different from the formula for the volume of a hemisphere.
Q: How do I round the answer to the nearest tenth?
A: To round the answer to the nearest tenth, you need to look at the digit in the hundredths place. If it is 5 or greater, you round up. If it is less than 5, you round down.
Q: What is the volume of a hemisphere with a radius of 5 ft?
A: To calculate the volume of a hemisphere with a radius of 5 ft, you need to plug in the value of the radius into the formula V = (2/3)πr³ and perform the necessary calculations.
V = (2/3) × 3.14159 × (5)³ V = (2/3) × 3.14159 × 125 V = 2.0944 × 125 V = 262.2
Q: What is the volume of a hemisphere with a radius of 10 ft?
A: To calculate the volume of a hemisphere with a radius of 10 ft, you need to plug in the value of the radius into the formula V = (2/3)πr³ and perform the necessary calculations.
V = (2/3) × 3.14159 × (10)³ V = (2/3) × 3.14159 × 1000 V = 2.0944 × 1000 V = 2094.4
Conclusion
In this article, we answered some frequently asked questions (FAQs) about the volume of a hemisphere. We provided step-by-step solutions to the problems of finding the volume of a hemisphere with a radius of 5 ft and 10 ft. We also discussed the formula for the volume of a hemisphere and how to round the answer to the nearest tenth.
Additional Information
- The formula for the volume of a hemisphere is V = (2/3)πr³.
- The radius of a hemisphere is the distance from the center of the hemisphere to the edge of the hemisphere.
- The volume of a hemisphere is always greater than the volume of a sphere with the same radius.
References
- "Mathematics for Dummies" by Mary Jane Sterling
- "Geometry: A Comprehensive Introduction" by Dan Pedoe
Related Topics
- Calculating the volume of a sphere
- Understanding the formula for the volume of a hemisphere
- Solving problems involving the volume of a hemisphere