To find the surface area of a cylinder, we can use the following formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- Height \( h = 40 \) in,
- Diameter \( d = 25 \) in, which means the radius \( r = \frac{d}{2} = \frac{25}{2} = 12.5 \) in.
Now, plug these values into the surface area formula:
\[ \text{Surface Area} = 2\pi (12.5)(40 + 12.5) \]
First, calculate \( 40 + 12.5 \):
\[ 40 + 12.5 = 52.5 \]
Now substitute it back into the formula:
\[ \text{Surface Area} = 2\pi (12.5)(52.5) \]
Now calculate \( 2 \times 12.5 \times 52.5 \):
\[ 2 \times 12.5 = 25 \]
\[ 25 \times 52.5 = 1312.5 \]
Now substitute this into the surface area expression:
\[ \text{Surface Area} = 1312.5\pi \]
Now to find the numerical value, we can approximate \( \pi \approx 3.14 \):
\[ \text{Surface Area} \approx 1312.5 \times 3.14 \approx 4127.25 \]
Rounding to the nearest whole number:
\[ \text{Surface Area} \approx 4127 \]
Therefore, the surface area of the cylinder is approximately 4127 square inches.
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