Practice Surface Area of a Cylinder in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The total area of the surface of a cylinder, consisting of two circular bases and a rectangular lateral surface that wraps around.

Imagine peeling the label off a can of soup. The label is a rectangle whose width is the circumference of the can (2πr2\pi r) and whose height is the can's height (hh). Add the two circular lids (top and bottom), and you have the total surface area.

Showing a random 20 of 50 problems.

Example 1

medium
If a cylinder's radius and height are both doubled, the total surface area is multiplied by what factor?

Example 2

medium
Express the total surface area of a cylinder of fixed volume VV and radius rr in terms of rr.

Example 3

medium
Two cylinders have the same height but radii 2 and 6. Find the ratio of their lateral surface areas.

Example 4

medium
Two cylinders have the same radius r=4r = 4 but heights 55 and 99. Find the ratio of their lateral surface areas.

Example 5

challenge
A closed cylindrical can holds volume 250π250\pi. Find the radius minimizing its total surface area.

Example 6

challenge
A closed cylindrical can must hold volume V=16πV = 16\pi. Express total surface area in terms of r and find the r minimizing it.

Example 7

easy
A can has diameter 88 cm and height 1010 cm. Find its total surface area in terms of π\pi.

Example 8

challenge
A closed cylindrical can of fixed surface area SS has volume V(r)=r(S−2πr2)2V(r) = \frac{r(S - 2\pi r^2)}{2}. Find the value of rr that maximizes VV.

Example 9

easy
A can has one lid (top open). Radius 3, height 7. Find its surface area in terms of π\pi.

Example 10

easy
A cylindrical mug (open top, closed bottom) has radius 33 and height 88. Find its outer surface area in terms of π\pi.

Example 11

medium
A cylindrical water tank (closed both ends) has r=10r = 10 ft, h=14h = 14 ft. How much paint, in square feet, covers the outside? (Use π≈3.14\pi \approx 3.14.)

Example 12

easy
What is the formula for the total surface area of a cylinder?

Example 13

medium
A cylindrical silo has r=4r = 4 m and h=10h = 10 m. Paint covers 5050 m2^2 per gallon. How many gallons cover its lateral surface? (Use π≈3.14\pi \approx 3.14.)

Example 14

medium
A cylinder has total surface area 54π54\pi and radius 3. Find its height.

Example 15

easy
When you peel the label off a can and lay it flat, what shape is it?

Example 16

medium
A pipe (hollow open cylinder) has radius 22 and length 1515. Find its surface area in terms of π\pi (lateral only).

Example 17

hard
A cylinder's height equals its diameter. If the total surface area is 108π108\pi cm², find the radius.

Example 18

medium
A cylinder has lateral surface area 48π48\pi and height 6. Find its radius.

Example 19

hard
A cylindrical tube (open both ends) has outer radius 66, inner radius 55, length 1212. Find the total surface area in terms of π\pi.

Example 20

hard
A cylinder has total surface area 24π24\pi. If r=1r = 1, find hh.
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