Ok, let's look at how you figure this problem out, and then we'll plug in the numbers.
Surface area = A(top) + A(bottom) + A(side)
A(top or bottom) = π r^2
A (side) = Circumference of base x Height = 2 π r x H
We know the total surface area is 260 cm^2.
Step 1: Figure out surface area of top and bottom
A (top or bottom) = π r^2 = 3.14 x 5^2 =
3.14 x 25 = 78.5 cm^2
Step 2: Subtract A(top) + A(bottom) from SA
260 cm^2 - 2(78.5 cm^2) =
260 - 157 = 103 cm^2
Step 3: Calculate Circumference of the Base
2 π r = 2 x 3.14 x 5 = 10 x 3.14 = 31.4 cm
Step 4: Divide balance of SA by C(base)
103 cm^2 / 31.4 cm = 3.28 cm
So, the Height of the cylinder is 3.28 cm