To calculate the surface area of a cylindrical drum, we 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:
- Diameter = 14 inches, therefore the radius \( r = \frac{14}{2} = 7 \) inches,
- Height \( h = 15 \) inches.
Now we can substitute these values into the formula:
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Calculate the area of the two circular bases: \[ 2\pi r^2 = 2\pi (7^2) = 2\pi (49) = 98\pi \approx 307.76 \text{ square inches} \]
-
Calculate the lateral surface area: \[ 2\pi rh = 2\pi (7)(15) = 210\pi \approx 659.73 \text{ square inches} \]
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Now add the areas together: \[ \text{Total Surface Area} = 98\pi + 210\pi = 308\pi \approx 967.65 \text{ square inches} \]
Rounding this to the nearest hundredth, we find:
\[ \text{Total Surface Area} \approx 967.61 \text{ square inches} \]
Thus, the approximate surface area of Tommy's drum is:
967.61 square inches.