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Find the surface area of a sphere witha diameter of 40 inches leave your answer in terms of pi

11 answers

To find the surface area of a sphere, you can use the formula:

\[ A = 4\pi r^2 \]

where \(A\) is the surface area and \(r\) is the radius of the sphere.

First, you need to calculate the radius from the given diameter. The radius is half of the diameter:

\[ r = \frac{\text{diameter}}{2} = \frac{40 \text{ inches}}{2} = 20 \text{ inches} \]

Now, substitute the radius into the surface area formula:

\[ A = 4\pi (20)^2 \]

Calculate \(20^2\):

\[ 20^2 = 400 \]

Now substitute this value back into the formula:

\[ A = 4\pi (400) \] \[ A = 1600\pi \]

Thus, the surface area of the sphere is

\[ \boxed{1600\pi} \text{ square inches.} \]

wrong

Let's go through the calculation of the surface area of the sphere again step by step.

The formula for the surface area (\(A\)) of a sphere is given by:

\[ A = 4\pi r^2 \]

  1. Find the radius: The diameter of the sphere is given as 40 inches. The radius \(r\) is half of the diameter:

\[ r = \frac{40 \text{ inches}}{2} = 20 \text{ inches} \]

  1. Substitute the radius into the formula:

\[ A = 4\pi (20)^2 \]

  1. Calculate \(20^2\):

\[ 20^2 = 400 \]

  1. Now substitute this value back into the formula:

\[ A = 4\pi (400) = 1600\pi \]

Thus, the surface area of the sphere is

\[ \boxed{1600\pi} \text{ square inches.} \]

If the calculation was still incorrect or if there was a specific aspect you think is erroneous, please clarify, and I'd be happy to address it!

wrong the answer is not 1600

I apologize for any confusion. Let's carefully recheck the calculation for the surface area of a sphere with a diameter of 40 inches.

  1. Given diameter: 40 inches

  2. Calculate the radius: \[ r = \frac{\text{diameter}}{2} = \frac{40}{2} = 20 \text{ inches} \]

  3. Use the surface area formula: \[ A = 4\pi r^2 \]

  4. Substituting the radius: \[ A = 4\pi (20)^2 \]

  5. Calculate \(20^2\): \[ (20)^2 = 400 \]

  6. Now substitute back into the formula: \[ A = 4\pi \times 400 = 1600\pi \]

Thus, the surface area of the sphere is indeed:

\[ \boxed{1600\pi} \text{ square inches.} \]

If there is a specific reason why you believe this answer is incorrect, please let me know, and we can clarify it further!

because ic hecke dit and it was wrong your so bad at math lol

I apologize for any confusion caused and appreciate your patience. Let me re-check the entire calculation again step by step to ensure accuracy.

  1. Given: Diameter of the sphere = 40 inches.

  2. Calculate the radius: \[ r = \frac{\text{diameter}}{2} = \frac{40 \text{ inches}}{2} = 20 \text{ inches} \]

  3. Use the surface area formula: \[ A = 4\pi r^2 \]

  4. Substituting the radius: \[ A = 4\pi (20)^2 \]

  5. Calculate \(20^2\): \[ (20)^2 = 400 \]

  6. Now substitute this back into the surface area formula: \[ A = 4\pi \times 400 \]

  7. Calculate: \[ A = 1600\pi \]

The final answer for the surface area of the sphere is:

\[ \boxed{1600\pi} \text{ square inches.} \]

If my calculations are consistent with previous responses and you believe there is a mistake, please help me understand where the discrepancy is coming from. Thank you!

LET ME READ IT TO YOU AGAIN.
FIND THE SURFACE AREA OF A SPHERE WITH A DIAMETER OF 40 INCHES. LEAVE YOUR ANSWER IN TERMS OF PI

Thank you for your patience. Let’s carefully go through the calculation again for the surface area of a sphere with a diameter of 40 inches, ensuring clarity and accuracy.

  1. Given diameter: 40 inches.

  2. Calculate the radius: \[ r = \frac{\text{diameter}}{2} = \frac{40 \text{ inches}}{2} = 20 \text{ inches} \]

  3. Use the surface area formula for a sphere: \[ A = 4\pi r^2 \]

  4. Substituting the radius into the formula: \[ A = 4\pi (20)^2 \]

  5. Calculating \(20^2\): \[ (20)^2 = 400 \]

  6. Continuing with the substitution: \[ A = 4\pi \times 400 \]

  7. Calculating the multiplication: \[ A = 1600\pi \]

Therefore, the surface area of the sphere is:

\[ \boxed{1600\pi} \text{ square inches.} \]

If there is still an issue with this computation or a misunderstanding, please clarify or share the expected result, and I'll do my best to address it. Thank you!

you suck and the answerr is wrong its not 1600

I sincerely apologize for any frustration caused by my previous responses. Let's work through this again from the beginning, step by step, to ensure we arrive at the correct answer.

  1. Given: The diameter of the sphere is 40 inches.

  2. Finding the radius: \[ r = \frac{\text{diameter}}{2} = \frac{40}{2} = 20 \text{ inches} \]

  3. Using the formula for the surface area of a sphere: \[ A = 4\pi r^2 \]

  4. Substituting the radius into the formula: \[ A = 4\pi (20)^2 \]

  5. Calculating \( (20)^2 \): \[ (20)^2 = 400 \]

  6. Now substituting back into the formula: \[ A = 4\pi \times 400 \]

  7. Calculating: \[ A = 1600\pi \]

Thus, the surface area of the sphere is \( \boxed{1600\pi} \text{ square inches.} \)

If you have a different calculation or expectation in mind, please let me know how you arrived at that conclusion, and I'll be glad to assist further and clarify. Thank you for your understanding.