Calculate the surface area of cylinders

Surface area of a closed right circular cylinder is the sum of the two congruent circular bases and the curved lateral surface: $SA=2\pi r^2+2\pi rh$ , where the lateral area can be interpreted as a rectangle with dimensions circumference $2\pi r$ and height $h$ . Learners distinguish area from volume, use consistent linear units and square units, and find exact or appropriately rounded values from radius, diameter, or height; oblique, composite, and calculus-based surface-area cases are not included.

Detailed Explanation: Calculate the surface area of cylinders

A closed cylinder has two circular bases and one curved surface.

The two bases have total area $2\pi r^2$ .
The curved surface has area $2\pi rh$ , because it can be unwrapped into a rectangle with width $2\pi r$ (the circumference) and height $h$ .

Therefore, use

SA=2\pi r^2+2\pi rh

where $r$ is the radius and $h$ is the height. The answer is in square units, not cubic units.

Example: Find the surface area of a closed cylinder with diameter $10\text{ cm}$ and height $12\text{ cm}$ . Give the exact answer and an approximation.

Step 1: Find the radius.

The radius is half the diameter:

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

The height is

h=12\text{ cm}

Step 2: Substitute into the formula.

SA=2\pi(5)^2+2\pi(5)(12)

Step 3: Calculate each part.

Area of the two circular bases:

2\pi(5)^2=50\pi

Area of the curved surface:

2\pi(5)(12)=120\pi

Step 4: Add the areas.

SA=50\pi+120\pi=170\pi\text{ cm}^2

This is the exact surface area. Using $\pi\approx3.14$ :

SA\approx170(3.14)=533.8\text{ cm}^2

So, the surface area is

\boxed{170\pi\text{ cm}^2\approx533.8\text{ cm}^2}

Learn by doing: Calculate the surface area of cylinders

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Surface Area - Cylinder - Image to Decimal

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Calculate the surface area of cylinders

Detailed Explanation: Calculate the surface area of cylinders

Learn by doing: Calculate the surface area of cylinders

Practice with unlimited practice problems

Practice:

Surface Area - Cylinder - Image to Decimal