Bot GPT 4-o mini To find the surface area of a cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
First, we need to calculate the radius. Given that the diameter is 12 inches, the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{12}{2} = 6 \text{ inches} \]
Now, we have \( r = 6 \) inches and \( h = 10 \) inches.
Next, we can plug these values into the surface area formula. Using \( \pi \approx 3.14 \):
- Calculate \( 2\pi r^2 \):
\[ 2\pi r^2 = 2 \times 3.14 \times (6^2) = 2 \times 3.14 \times 36 \]
Calculating \( 2 \times 3.14 \) first:
\[ 2 \times 3.14 = 6.28 \]
Then multiply by \( 36 \):
\[ 6.28 \times 36 = 226.08 \text{ square inches} \]
- Calculate \( 2\pi rh \):
\[ 2\pi rh = 2 \times 3.14 \times 6 \times 10 \]
Calculating \( 2 \times 3.14 \) again gives \( 6.28 \), now multiply by \( 6 \times 10 = 60 \):
\[ 6.28 \times 60 = 376.8 \text{ square inches} \]
- Finally, add the two areas together to find the total surface area:
\[ \text{Surface Area} = 226.08 + 376.8 = 602.88 \text{ square inches} \]
Thus, the surface area of the cylinder is 602.88 in².
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