find the surface area of a sphere with a diameter of 40 inches. leave your answer in terms of pi
its 1600π
The formula to calculate the surface area of a sphere is given by:
Surface Area = 4πr²
But we're given the diameter of the sphere, which is twice the radius (d = 2r). Therefore, if the diameter (d) is 40 inches, the radius (r) will be half of that, which is 20 inches.
Now let's plug in the radius into the formula:
Surface Area = 4π(20 inches)²
= 4π(400 inches²)
= 1600π inches²
So, the surface area of the sphere is 1600π square inches.
Apologies for any confusion. Let's make sure we get it right.
To find the surface area of the sphere, we still use the formula:
Surface Area = 4πr²
Given the diameter is 40 inches, the radius r will indeed be half of that, which is:
r = diameter / 2
r = 40 inches / 2
r = 20 inches
So, the radius is 20 inches. Plugging this into the formula:
Surface Area = 4π(20 inches)²
Surface Area = 4π(400 inches²)
Surface Area = 1600π inches²
Therefore, the surface area of the sphere with a diameter of 40 inches is indeed 1600π square inches. If the original calculation seemed incorrect, please verify this result against the surface area of a sphere formula and the given measurements. If this still doesn't solve your query, could you specify what the expected answer should be, or provide additional context?
I apologize for any confusion that may have occurred due to the way I presented the answer. When you asked to leave the answer in terms of pi, I should have made it clear that the pi symbol (π) remains symbolic in the answer and is not replaced with an approximate decimal value. The correct surface area of the sphere, leaving π as a symbol and without multiplying it out, is indeed:
Surface Area = 1600π square inches
This means we leave π as is, without converting it to its approximate decimal value (approximately 3.14159). The expression "1600π square inches" is the exact surface area in terms of π.
Apologies for any confusion earlier. Let's do the calculation one last time to ensure accuracy.
Given:
Diameter = 40 inches
Radius r = Diameter / 2 = 40 inches / 2 = 20 inches
Formula for the surface area (A) of a sphere:
A = 4πr²
Plug in the radius:
A = 4π(20 inches)²
A = 4π(400 inches²)
A = 1600π inches²
The correct surface area of the sphere, in terms of π, is indeed 1600π square inches. If you are seeking a different answer, please ensure the given information (diameter of 40 inches) is correct. If there is another formulation or context, please provide it for further clarification.
I apologize for the oversight. Let's go through the calculation again step by step:
1. Find the radius (r) of the sphere using the diameter (d):
Since the diameter d is 40 inches, we divide by 2 to find the radius:
\( r = \frac{d}{2} = \frac{40 \text{ inches}}{2} = 20 \text{ inches} \)
2. Use the formula for the surface area (SA) of a sphere:
\( SA = 4\pi r^2 \)
3. Plug in the radius (r):
\( SA = 4\pi (20 \text{ inches})^2 \)
\( SA = 4\pi (400 \text{ inches}^2) \)
\( SA = 1600\pi \text{ inches}^2 \)
It appears that the calculations we’ve provided are correct, and the surface area of the sphere is \( 1600\pi \text{ inches}^2 \), given the diameter of 40 inches. This is the correct answer expressed in terms of pi. If there is specific criteria or context that hasn't been discussed, please provide that so I can give you the answer you expect. Otherwise, the answer as calculated above is correct based on standard mathematical principles.
you got 1600 did you leave the answer in terms of pi?
nope still wrong what do i do to make the answer right instead of wrong
anways its okay another question is to find the surface area of a sphere with a radius of 3.6 use 3.14 for pi and round your answer to the nearest hundredth if necessary
To calculate the surface area of a sphere when given the radius, you use the formula:
Surface Area (SA) = 4πr²
In this case, you're given the radius (r) as 3.6 units and are instructed to use 3.14 as the value for π (pi). Let's plug in these values into the formula:
SA = 4 * 3.14 * (3.6)²
Now, let's calculate step by step:
1. Square the radius:
(3.6)² = 3.6 * 3.6 = 12.96
2. Multiply this by 4 and π (approximated as 3.14):
4 * 3.14 * 12.96 = 162.2784
Now, we'll round to the nearest hundredth:
SA ≈ 162.28 (rounded to two decimal places)
The surface area of the sphere with a radius of 3.6 units using 3.14 for π, and rounded to the nearest hundredth, is approximately 162.28 square units.