Problem

Find the surface area of a cylinder with a base radius of $3 \mathrm{yd}$ and a height of $7 \mathrm{yd}$. Write your answer in terms of $\pi$, and be sure to include the correct unit.

Answer

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Answer

Final Answer: The surface area of the cylinder is \(\boxed{60\pi \, \text{yd}^2}\).

Steps

Step 1 :Given a cylinder with a base radius of 3 yd and a height of 7 yd, we are to find the surface area. The formula for the surface area of a cylinder is \(2\pi r(r + h)\), where \(r\) is the radius of the base and \(h\) is the height of the cylinder.

Step 2 :Substitute \(r = 3\) yd and \(h = 7\) yd into the formula to find the surface area.

Step 3 :Calculate the surface area to get approximately 188.5 square yards.

Step 4 :However, the question asks for the answer in terms of \(\pi\), so we need to express this decimal as a fraction of \(\pi\).

Step 5 :Calculate the surface area in terms of \(\pi\) to get approximately 60\(\pi\) square yards. This is very close to an integer, so it's likely that the exact surface area is 60\(\pi\) square yards.

Step 6 :Final Answer: The surface area of the cylinder is \(\boxed{60\pi \, \text{yd}^2}\).

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