A cylinder with a radius of 2 yd and a height of
3 yd.

20 π

Step-by-step explanation:

The surface area of a cylinder is made up of 2 circles and its side.

To find the circles' areas, use the area formula for a circle: A = π.

Since our radius is 2 yd, we can substitute r = 2 into this formula.

A = π = 4π

Now remember, this is only the area of once circle. Multiply 4π by 2 to get the area of both circles: 8π.

Now we need to find the surface area of the side.

If we flatten it out, we can see that the side is actually a curled up rectangle.

The length is the circumference of the circle and the width is the height of the cylinder.

To find the circumference, use the circumference formula for a circle: C = 2πr.

Substitute r = 2 into the formula.

C = 2π2 = 4π

Now that we know that the length is 4π, we can multiply the length by the width to find the area of the cylinder's side.

l = 4π

w = 3

A = lw = 4π * 3 = 12π

Finally, we can add the areas of the circles and the side to get the total surface area.

8π + 12π  = 20π

And that is your answer!

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step-by-step explanation: