### Video Transcript

Calculate the lateral surface area
of the cylinder below rounded to one decimal place.

The lateral surface area of a
cylinder is the area of the curved surface that wraps around the cylinder. If we were to unwrap this surface,
we would see that it is a rectangle. The length of the rectangle is the
same as the circumference of the cylinder’s circular base. And the width is equal to the
cylinder’s height. The area of a rectangle is of
course equal to its length multiplied by its width. So the lateral surface area of a
cylinder is therefore equal to two 𝜋𝑟ℎ, where 𝑟 represents the base radius of the
cylinder and ℎ represents the height.

We’ve been given the height in the
figure. It’s 13 centimeters. We have to be a little careful
because we’ve been given the diameter, rather than the radius, of the circular
base. Recalling that the radius is half
the diameter, we have that the radius of the cylinder is five centimeters. Substituting both of these values
into the formula for the lateral surface area gives two 𝜋 multiplied by five
multiplied by 13. This simplifies to 130𝜋.

If we were required to give our
answer in an exact form, we could leave it like this. But we’re asked to round the answer
to one decimal place. So we’ll go on and evaluate this as
a decimal. It’s equal to 408.4070
continuing. Rounding as required and including
the units for area, we have that the lateral surface area of the given cylinder to
one decimal place is 408.4 square centimeters.