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 of the cylinder
- \( h \) is the height of the cylinder
Given that the diameter of the cylinder is 12 inches, the radius \( r \) is half of the diameter:
\[ r = \frac{12}{2} = 6 \text{ inches} \]
The height \( h \) is given as 10 inches. Now, we can substitute these values into the surface area formula.
- Calculate the area of the two circular bases:
\[ 2\pi r^2 = 2 \times 3.14 \times (6)^2 \] \[ = 2 \times 3.14 \times 36 \] \[ = 2 \times 113.04 = 226.08 \text{ in}^2 \]
- Calculate the area of the curved surface:
\[ 2\pi rh = 2 \times 3.14 \times 6 \times 10 \] \[ = 2 \times 3.14 \times 60 \] \[ = 2 \times 188.4 = 376.8 \text{ in}^2 \]
- Now add the areas of the bases and the curved surface:
\[ \text{Surface Area} = 226.08 + 376.8 = 602.88 \text{ in}^2 \]
Therefore, the surface area of the cylinder is:
\[ \boxed{602.88} \text{ in}^2 \]
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