Skill: Calculate the surface area of cylinders

A cylinder has:

• two circular bases, each with area $\pi r^2$
• one curved surface, which unwraps into a rectangle with area $2\pi rh$

So, the total surface area is

$$S=2\pi r^2+2\pi rh$$

where $r$ is the radius and $h$ is the height. The answer is always in square units.

Example: Find the surface area of a cylinder with diameter $10$ cm and height $7$ cm.

1. Find the radius. The radius is half the diameter:

$$r=\frac{10}{2}=5\text{ cm}$$

2. Substitute $r=5$ and $h=7$ into the formula:

$$S=2\pi(5)^2+2\pi(5)(7)$$

3. Simplify each part:

$$S=2\pi(25)+70\pi$$ $$S=50\pi+70\pi=120\pi$$

Therefore, the exact surface area is

$$\boxed{120\pi\text{ cm}^2}$$

Using $\pi\approx3.14$, the surface area is approximately

$$120(3.14)=376.8\text{ cm}^2$$

So, the surface area is about $\boxed{376.8\text{ cm}^2}$.