Question
Find the surface area of this cylinder and round to the nearest whole number. (The answer isn't 4125 square inches)
25 in, 40 in
25 in, 40 in
Answers
GPT-4o mini
To find the surface area of a cylinder, we 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.
From the dimensions provided, it looks like:
- The diameter of the cylinder is 25 inches, so the radius \( r \) is:
\[
r = \frac{25}{2} = 12.5 \text{ inches}
\]
- The height \( h \) of the cylinder is 40 inches.
Now we can substitute these values into the surface area formula:
\[
\text{Surface Area} = 2\pi(12.5)(40 + 12.5)
\]
Calculating \( h + r \):
\[
h + r = 40 + 12.5 = 52.5 \text{ inches}
\]
Now substituting back into the formula:
\[
\text{Surface Area} = 2\pi(12.5)(52.5)
\]
Now calculating \( 2\pi(12.5)(52.5) \):
1. Calculate \( 12.5 \times 52.5 \):
\[
12.5 \times 52.5 = 656.25
\]
2. Now multiply by \( 2\pi \):
\[
\text{Surface Area} = 2 \times \pi \times 656.25 \approx 2 \times 3.14159265 \times 656.25 \approx 4125.44
\]
Finally, rounding to the nearest whole number:
\[
\text{Surface Area} \approx 4125
\]
You mentioned that the answer isn't 4125 square inches, suggesting there may be a misunderstanding. The calculated surface area \( \approx 4125 \) square inches is correct based on the dimensions provided. Please check if the values of diameter and height were correctly identified.
\[
\text{Surface Area} = 2\pi r(h + r)
\]
where \( r \) is the radius and \( h \) is the height of the cylinder.
From the dimensions provided, it looks like:
- The diameter of the cylinder is 25 inches, so the radius \( r \) is:
\[
r = \frac{25}{2} = 12.5 \text{ inches}
\]
- The height \( h \) of the cylinder is 40 inches.
Now we can substitute these values into the surface area formula:
\[
\text{Surface Area} = 2\pi(12.5)(40 + 12.5)
\]
Calculating \( h + r \):
\[
h + r = 40 + 12.5 = 52.5 \text{ inches}
\]
Now substituting back into the formula:
\[
\text{Surface Area} = 2\pi(12.5)(52.5)
\]
Now calculating \( 2\pi(12.5)(52.5) \):
1. Calculate \( 12.5 \times 52.5 \):
\[
12.5 \times 52.5 = 656.25
\]
2. Now multiply by \( 2\pi \):
\[
\text{Surface Area} = 2 \times \pi \times 656.25 \approx 2 \times 3.14159265 \times 656.25 \approx 4125.44
\]
Finally, rounding to the nearest whole number:
\[
\text{Surface Area} \approx 4125
\]
You mentioned that the answer isn't 4125 square inches, suggesting there may be a misunderstanding. The calculated surface area \( \approx 4125 \) square inches is correct based on the dimensions provided. Please check if the values of diameter and height were correctly identified.