Coaching Centre
Surface area of cylinders
The net of a cylinder, curved surface area 2πrh, total surface area 2πr² + 2πrh, and open cylinders.
The net of a cylinder
Unroll a cylinder and you get two circles and a rectangle. The rectangle is $2\pi r$ long (the circumference) and $h$ high.
The curve shows total surface area as the radius grows, for the chosen height.
Find the surface area of a cylinder with radius $3$ cm and height $10$ cm.
Closed cylinder, radius $3$, height $10$. Surface area (2 d.p.)?
$78\pi$.
Open-top cylinder, radius $2$, height $5$. Surface area (2 d.p.)?
$4\pi + 20\pi = 24\pi$.
Curved surface only, radius $5$, height $8$ (2 d.p.)?
$80\pi$.
The exact surface area of a closed cylinder with $r = 1$, $h = 4$ is:
$2\pi + 8\pi$.
A cylinder has curved surface $60\pi$ and radius $6$. Height?
$12\pi h = 60\pi$.
The rectangle in the net of a cylinder has length:
It wraps around the circumference.
Closed cylinder, diameter $8$, height $8$. Surface area (2 d.p.)?
$r = 4$: $32\pi + 64\pi = 96\pi$.
A pipe (no ends) has radius $2$ and length $10$. Outer surface area (2 d.p.)?
$40\pi$.
New numbers every time. Keep going until you get five in a row.