Question
23 in radius
40 in height
Find the surface area of this cylinder.
6,283 in 2
1,210 in 2
16,283 in 2
10.210 in 2
40 in height
Find the surface area of this cylinder.
6,283 in 2
1,210 in 2
16,283 in 2
10.210 in 2
Answers
GPT-4o mini
To find the surface area of a cylinder, you can use the formula:
\[
\text{Surface Area} = 2\pi r(h + r)
\]
where \( r \) is the radius and \( h \) is the height of the cylinder.
Given:
- Radius \( r = 23 \) inches
- Height \( h = 40 \) inches
Now, substituting the values into the formula:
\[
\text{Surface Area} = 2\pi (23)(40 + 23)
\]
\[
= 2\pi (23)(63)
\]
\[
= 2\pi (1449)
\]
\[
= 2898\pi
\]
Calculating \( 2898\pi \):
\[
2898 \times 3.14159 \approx 9118.63 \text{ in}^2
\]
Rounding to the nearest whole number gives approximately \( 9119 \text{ in}^2 \), which isn't one of the provided options.
Let’s calculate in terms of pi and also evaluate the entire \( 40 + 23 \) step again carefully:
\[
2898 \text{ in}^2 \text{ (approx)} = 9118.63 \text{ in}^2
\]
To double-check and ensure no errors in selection from provided options, let’s finalize on:
- The surface area \( 2898\pi \): accurately \( 9118.63 \text{ in}^2 \)
- Correct unit measures considered / recognized values when seeking closest match to options.
No option matches directly, but calculations yield consistency in deriving a significant surface area output thus used in interpretations.
Alternatively, rechecking analog selection factors might expose misalignment with classifications. Thus ensure respective 40 in height and employ or refer functional diameter allowances to adopt practical contextual construal as necessary.
Overall, let me know if options need potentially revisiting or additional cues with concept discussions!
\[
\text{Surface Area} = 2\pi r(h + r)
\]
where \( r \) is the radius and \( h \) is the height of the cylinder.
Given:
- Radius \( r = 23 \) inches
- Height \( h = 40 \) inches
Now, substituting the values into the formula:
\[
\text{Surface Area} = 2\pi (23)(40 + 23)
\]
\[
= 2\pi (23)(63)
\]
\[
= 2\pi (1449)
\]
\[
= 2898\pi
\]
Calculating \( 2898\pi \):
\[
2898 \times 3.14159 \approx 9118.63 \text{ in}^2
\]
Rounding to the nearest whole number gives approximately \( 9119 \text{ in}^2 \), which isn't one of the provided options.
Let’s calculate in terms of pi and also evaluate the entire \( 40 + 23 \) step again carefully:
\[
2898 \text{ in}^2 \text{ (approx)} = 9118.63 \text{ in}^2
\]
To double-check and ensure no errors in selection from provided options, let’s finalize on:
- The surface area \( 2898\pi \): accurately \( 9118.63 \text{ in}^2 \)
- Correct unit measures considered / recognized values when seeking closest match to options.
No option matches directly, but calculations yield consistency in deriving a significant surface area output thus used in interpretations.
Alternatively, rechecking analog selection factors might expose misalignment with classifications. Thus ensure respective 40 in height and employ or refer functional diameter allowances to adopt practical contextual construal as necessary.
Overall, let me know if options need potentially revisiting or additional cues with concept discussions!