# The total surface area of a cylinder is 260 cm^2. If the radius of it' base is 5 cm, find it's length.

## Expert Answers

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

Approved by eNotes Editorial Team

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