Area And VolumeVolume Of A SphereThe Diameter, D D D , Of A Sphere Is 9.6 Mm. Calculate The Sphere's Volume, V V V .Use The Value 3.14 For Π \pi Π , And Round Your Answer To The Nearest Tenth. (Do Not Round Any Intermediate
Introduction
In mathematics, the volume of a sphere is a fundamental concept that has numerous applications in various fields, including physics, engineering, and architecture. The volume of a sphere is calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. In this article, we will explore how to calculate the volume of a sphere using the given diameter and the value of π.
Understanding the Formula
The formula for the volume of a sphere is V = (4/3)πr^3. To calculate the volume, we need to know the radius of the sphere. However, we are given the diameter of the sphere, which is 9.6 mm. We can use the formula D = 2r to find the radius of the sphere.
Calculating the Radius
The formula D = 2r can be rearranged to find the radius: r = D/2. Substituting the given diameter of 9.6 mm, we get:
r = 9.6 mm / 2 r = 4.8 mm
Calculating the Volume
Now that we have the radius, we can calculate the volume of the sphere using the formula V = (4/3)πr^3. Substituting the value of π as 3.14 and the radius as 4.8 mm, we get:
V = (4/3) × 3.14 × (4.8 mm)^3 V = (4/3) × 3.14 × 112.896 V = 4.1888 × 112.896 V = 473.11 mm^3
Rounding the Answer
We are asked to round the answer to the nearest tenth. Therefore, we round 473.11 mm^3 to 473.1 mm^3.
Conclusion
In this article, we calculated the volume of a sphere using the given diameter and the value of π. We first found the radius of the sphere using the formula D = 2r, and then used the formula V = (4/3)πr^3 to calculate the volume. Finally, we rounded the answer to the nearest tenth.
Real-World Applications
The volume of a sphere has numerous real-world applications, including:
- Physics: The volume of a sphere is used to calculate the volume of a planet or a star.
- Engineering: The volume of a sphere is used to calculate the volume of a tank or a container.
- Architecture: The volume of a sphere is used to calculate the volume of a building or a structure.
Example Problems
Here are some example problems that you can try:
- Problem 1: A sphere has a diameter of 12 mm. Calculate its volume using the value 3.14 for π.
- Problem 2: A sphere has a radius of 5 mm. Calculate its volume using the value 3.14 for π.
- Problem 3: A sphere has a diameter of 18 mm. Calculate its volume using the value 3.14 for π.
Solutions
Here are the solutions to the example problems:
- Problem 1: r = 12 mm / 2 = 6 mm. V = (4/3) × 3.14 × (6 mm)^3 = 904.32 mm^3.
- Problem 2: V = (4/3) × 3.14 × (5 mm)^3 = 523.60 mm^3.
- Problem 3: r = 18 mm / 2 = 9 mm. V = (4/3) × 3.14 × (9 mm)^3 = 3050.88 mm^3.
Conclusion
Q: What is the formula for calculating the volume of a sphere?
A: The formula for calculating the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
Q: How do I find the radius of a sphere if I only know its diameter?
A: To find the radius of a sphere, you can use the formula D = 2r, where D is the diameter of the sphere. Rearranging this formula, you get r = D/2.
Q: What is the value of π that I should use when calculating the volume of a sphere?
A: The value of π that you should use when calculating the volume of a sphere is 3.14.
Q: Can I use a calculator to calculate the volume of a sphere?
A: Yes, you can use a calculator to calculate the volume of a sphere. Simply enter the value of the radius and the value of π, and the calculator will give you the volume.
Q: How do I round the answer to the nearest tenth when calculating the volume of a sphere?
A: To round the answer to the nearest tenth, you can look at the hundredth place value. If the hundredth place value is 5 or greater, you round up. If the hundredth place value is 4 or less, you round down.
Q: What are some real-world applications of calculating the volume of a sphere?
A: Some real-world applications of calculating the volume of a sphere include:
- Physics: Calculating the volume of a planet or a star.
- Engineering: Calculating the volume of a tank or a container.
- Architecture: Calculating the volume of a building or a structure.
Q: Can I calculate the volume of a sphere if I only know its circumference?
A: No, you cannot calculate the volume of a sphere if you only know its circumference. You need to know the radius of the sphere to calculate its volume.
Q: How do I calculate the volume of a sphere if I know its surface area?
A: You cannot calculate the volume of a sphere if you only know its surface area. You need to know the radius of the sphere to calculate its volume.
Q: Can I use a formula to calculate the volume of a sphere if I know its diameter and surface area?
A: No, you cannot use a formula to calculate the volume of a sphere if you know its diameter and surface area. You need to know the radius of the sphere to calculate its volume.
Q: What is the relationship between the volume of a sphere and its diameter?
A: The volume of a sphere is proportional to the cube of its diameter. This means that if you double the diameter of a sphere, its volume will increase by a factor of 8.
Q: Can I calculate the volume of a sphere if I know its height and width?
A: No, you cannot calculate the volume of a sphere if you only know its height and width. You need to know the radius of the sphere to calculate its volume.
Q: How do I calculate the volume of a sphere if I know its volume and surface area?
A: You cannot calculate the radius of a sphere if you only know its volume and surface area. You need to know the radius of the sphere to calculate its volume.
Conclusion
In this article, we answered some frequently asked questions about calculating the volume of a sphere. We covered topics such as the formula for calculating the volume of a sphere, finding the radius of a sphere, and real-world applications of calculating the volume of a sphere. We also covered some common misconceptions and provided examples to help illustrate the concepts.