Select The Correct Answer From The Drop-down Menu.A Sphere Has A Radius Of 24 Centimeters. What Is Its Volume?$\[ V = \square \pi \, \text{cm}^3 \\]
Introduction
In mathematics, the volume of a sphere is a fundamental concept that is used to calculate the amount of space inside a sphere. The formula for the volume of a sphere is given by V = (4/3)πr^3, where r is the radius of the sphere. In this article, we will use this formula to calculate the volume of a sphere with a radius of 24 centimeters.
Understanding the Formula
The formula for the volume of a sphere is V = (4/3)πr^3. This formula is derived from the fact that the volume of a sphere is proportional to the cube of its radius. The constant of proportionality is (4/3)π.
Calculating the Volume
To calculate the volume of a sphere with a radius of 24 centimeters, we can plug this value into the formula:
V = (4/3)π(24)^3
Step 1: Calculate the Cube of the Radius
First, we need to calculate the cube of the radius:
(24)^3 = 13824
Step 2: Multiply by (4/3)π
Next, we multiply the cube of the radius by (4/3)π:
(4/3)π(13824) = (4/3) × 3.14159 × 13824
Step 3: Calculate the Final Answer
Using a calculator, we can calculate the final answer:
(4/3) × 3.14159 × 13824 ≈ 298598.4
Conclusion
In this article, we used the formula V = (4/3)πr^3 to calculate the volume of a sphere with a radius of 24 centimeters. We broke down the calculation into three steps: calculating the cube of the radius, multiplying by (4/3)π, and calculating the final answer. The final answer is approximately 298598.4 cubic centimeters.
Real-World Applications
The volume of a sphere has many real-world applications, such as:
- Calculating the volume of a ball or a sphere in a game or simulation
- Determining the amount of space inside a sphere-shaped container
- Calculating the volume of a planet or a moon
Common Mistakes
When calculating the volume of a sphere, it's easy to make mistakes. Here are some common mistakes to avoid:
- Forgetting to cube the radius
- Forgetting to multiply by (4/3)π
- Using the wrong value for π
Practice Problems
To practice calculating the volume of a sphere, try the following problems:
- A sphere has a radius of 12 centimeters. What is its volume?
- A sphere has a radius of 36 centimeters. What is its volume?
Conclusion
Q: What is the formula for the volume of a sphere?
A: The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
Q: How do I calculate the volume of a sphere with a radius of 10 centimeters?
A: To calculate the volume of a sphere with a radius of 10 centimeters, you can plug this value into the formula:
V = (4/3)π(10)^3
First, calculate the cube of the radius:
(10)^3 = 1000
Next, multiply the cube of the radius by (4/3)π:
(4/3)π(1000) = (4/3) × 3.14159 × 1000
Using a calculator, you can calculate the final answer:
(4/3) × 3.14159 × 1000 ≈ 4188.79
Q: What is the volume of a sphere with a radius of 20 centimeters?
A: To calculate the volume of a sphere with a radius of 20 centimeters, you can plug this value into the formula:
V = (4/3)π(20)^3
First, calculate the cube of the radius:
(20)^3 = 8000
Next, multiply the cube of the radius by (4/3)π:
(4/3)π(8000) = (4/3) × 3.14159 × 8000
Using a calculator, you can calculate the final answer:
(4/3) × 3.14159 × 8000 ≈ 33551.36
Q: How do I calculate the volume of a sphere with a radius of 5 centimeters?
A: To calculate the volume of a sphere with a radius of 5 centimeters, you can plug this value into the formula:
V = (4/3)π(5)^3
First, calculate the cube of the radius:
(5)^3 = 125
Next, multiply the cube of the radius by (4/3)π:
(4/3)π(125) = (4/3) × 3.14159 × 125
Using a calculator, you can calculate the final answer:
(4/3) × 3.14159 × 125 ≈ 523.60
Q: What is the volume of a sphere with a radius of 15 centimeters?
A: To calculate the volume of a sphere with a radius of 15 centimeters, you can plug this value into the formula:
V = (4/3)π(15)^3
First, calculate the cube of the radius:
(15)^3 = 3375
Next, multiply the cube of the radius by (4/3)π:
(4/3)π(3375) = (4/3) × 3.14159 × 3375
Using a calculator, you can calculate the final answer:
(4/3) × 3.14159 × 3375 ≈ 17771.45
Q: How do I calculate the volume of a sphere with a radius of 30 centimeters?
A: To calculate the volume of a sphere with a radius of 30 centimeters, you can plug this value into the formula:
V = (4/3)π(30)^3
First, calculate the cube of the radius:
(30)^3 = 27000
Next, multiply the cube of the radius by (4/3)π:
(4/3)π(27000) = (4/3) × 3.14159 × 27000
Using a calculator, you can calculate the final answer:
(4/3) × 3.14159 × 27000 ≈ 113097.33
Conclusion
In this article, we answered some frequently asked questions about calculating the volume of a sphere. We provided step-by-step instructions for calculating the volume of a sphere with different radii, and we also provided the final answers for each problem. We hope that this article has been helpful in understanding how to calculate the volume of a sphere.