Select The Correct Answer.The Diameter Of A Sphere Measures 10.4 Inches. What Is The Surface Area Of The Sphere?A. $216.32 \pi \, \text{in}^2$ B. $108.16 \pi \, \text{in}^2$ C. $432.64 \pi \, \text{in}^2$ D. $54.08 \pi
Understanding the Basics of a Sphere
A sphere is a three-dimensional shape that is perfectly round and has no edges or corners. It is a continuous curved surface that is symmetrical about its center. The surface area of a sphere is the total area of its curved surface. In this article, we will learn how to calculate the surface area of a sphere using its diameter.
The Formula for the Surface Area of a Sphere
The formula for the surface area of a sphere is given by:
A = 4Ï€r^2
where A is the surface area of the sphere, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.
Converting Diameter to Radius
The diameter of a sphere is twice its radius. Therefore, if we know the diameter of a sphere, we can easily find its radius by dividing the diameter by 2.
Given Data
The diameter of a sphere measures 10.4 inches. We need to find the surface area of the sphere.
Step 1: Convert Diameter to Radius
To find the radius of the sphere, we divide the diameter by 2:
r = diameter / 2 r = 10.4 / 2 r = 5.2 inches
Step 2: Calculate the Surface Area
Now that we have the radius of the sphere, we can use the formula for the surface area of a sphere to find the surface area:
A = 4Ï€r^2 A = 4Ï€(5.2)^2 A = 4Ï€(27.04) A = 108.16Ï€
Rounding the Answer
Since the answer choices are given in terms of π, we can round our answer to two decimal places:
A ≈ 108.16π
Selecting the Correct Answer
Comparing our answer with the answer choices, we can see that the correct answer is:
B.
Conclusion
In this article, we learned how to calculate the surface area of a sphere using its diameter. We used the formula for the surface area of a sphere and converted the diameter to radius to find the surface area. We also rounded our answer to two decimal places to match the answer choices. The correct answer is B. .
Additional Tips and Tricks
- Make sure to convert the diameter to radius before using the formula for the surface area of a sphere.
- Use the correct value of π (approximately 3.14) when calculating the surface area.
- Round your answer to two decimal places to match the answer choices.
Frequently Asked Questions
- What is the formula for the surface area of a sphere?
- The formula for the surface area of a sphere is A = 4Ï€r^2.
- How do I convert the diameter of a sphere to its radius?
- To convert the diameter to radius, divide the diameter by 2.
- What is the correct answer for the given problem?
- The correct answer is B. .
Frequently Asked Questions: Calculating the Surface Area of a Sphere ====================================================================
- The correct answer is B. .
Q: What is the formula for the surface area of a sphere?
A: The formula for the surface area of a sphere is A = 4πr^2, where A is the surface area of the sphere, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.
Q: How do I convert the diameter of a sphere to its radius?
A: To convert the diameter to radius, divide the diameter by 2. For example, if the diameter of a sphere is 10.4 inches, the radius would be 10.4 / 2 = 5.2 inches.
Q: What is the correct answer for the given problem?
A: The correct answer is B. .
Q: Why do I need to use the correct value of π when calculating the surface area?
A: Using the correct value of π is essential when calculating the surface area of a sphere. The value of π is approximately 3.14, and using this value will give you an accurate answer.
Q: Can I use a calculator to find the surface area of a sphere?
A: Yes, you can use a calculator to find the surface area of a sphere. Simply enter the radius of the sphere and the value of π, and the calculator will give you the surface area.
Q: What if I don't have a calculator? Can I still find the surface area of a sphere?
A: Yes, you can still find the surface area of a sphere without a calculator. You can use the formula A = 4Ï€r^2 and perform the calculations manually.
Q: How do I round my answer to two decimal places?
A: To round your answer to two decimal places, simply look at the third decimal place and decide whether to round up or down. If the third decimal place is 5 or greater, round up. If it's less than 5, round down.
Q: What if I get a different answer than the one given in the answer choices?
A: If you get a different answer than the one given in the answer choices, double-check your calculations to make sure you didn't make any mistakes. If you're still unsure, try using a calculator or asking a teacher or tutor for help.
Q: Can I use this formula to find the surface area of other shapes?
A: No, this formula is specifically for finding the surface area of a sphere. If you need to find the surface area of other shapes, you'll need to use a different formula.
Q: Where can I find more information about calculating the surface area of a sphere?
A: You can find more information about calculating the surface area of a sphere in your math textbook or online resources such as Khan Academy or Mathway.
Conclusion
Calculating the surface area of a sphere is a simple process that requires the use of the formula A = 4πr^2. By following the steps outlined in this article, you can easily find the surface area of a sphere and answer questions like the one given in the problem. Remember to use the correct value of π and round your answer to two decimal places to get an accurate answer.