Calculate the surface area of cylinders

Surface area of a cylinder is the total area of its two congruent circular bases and its curved lateral surface, represented by the net of two circles and a rectangle, giving $S=2\pi r^2+2\pi rh$ for radius $r$ and height $h$ . The quantities are interpreted in square units, with answers expressed exactly using $\pi$ or approximated appropriately; the diameter must be halved when a radius is required.

Detailed Explanation: 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.

Find the radius. The radius is half the diameter:

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

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

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

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 $\boxed{376.8\text{ cm}^2}$ .

Learn by doing: Calculate the surface area of cylinders

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Surface Area of a Cylinder - Calculate

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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

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Surface Area of a Cylinder - Calculate