To find the surface area of a cylinder, we use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius,
- \( h \) is the height.
From the problem:
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The width of the cylinder is given as 2 yards, which means the diameter of the cylinder is 2 yards. Therefore, the radius \( r \) is half of that: \[ r = \frac{2}{2} = 1 \text{ yard} \]
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The height \( h \) is given as 3 yards.
Now we can plug in the values into the surface area formula.
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Calculate \( 2\pi r^2 \): \[ 2\pi r^2 = 2 \times 3.14 \times (1)^2 = 2 \times 3.14 \times 1 = 6.28 \]
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Calculate \( 2\pi rh \): \[ 2\pi rh = 2 \times 3.14 \times 1 \times 3 = 2 \times 3.14 \times 3 = 18.84 \]
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Add both results to find the total surface area: \[ \text{Surface Area} = 6.28 + 18.84 = 25.12 \]
So, the surface area of the cylinder is 25.12 square yards.
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