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 ( $2\pi r$ ) and whose height is the can's height ( $h$ ). 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

V

and radius

r

in terms of

r

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 = 4

but heights

5

and

9

. Find the ratio of their lateral surface areas.

Example 5

challenge

A closed cylindrical can holds volume

250\pi

. Find the radius minimizing its total surface area.

Example 6

challenge

A closed cylindrical can must hold volume

V = 16\pi

. Express total surface area in terms of r and find the r minimizing it.

Example 7

easy

A can has diameter

8

cm and height

10

cm. Find its total surface area in terms of

\pi

Can: diameter 8 cm → r = 4 cm, h = 10 cm

Example 8

challenge

A closed cylindrical can of fixed surface area

S

has volume

V(r) = \frac{r(S - 2\pi r^2)}{2}

. Find the value of

r

that maximizes

V

Example 9

easy

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

\pi

One-lid cylinder: r = 3, h = 7

Example 10

easy

A cylindrical mug (open top, closed bottom) has radius

3

and height

8

. Find its outer surface area in terms of

\pi

Example 11

medium

A cylindrical water tank (closed both ends) has

r = 10

ft,

h = 14

ft. How much paint, in square feet, covers the outside? (Use

\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 = 4

m and

h = 10

m. Paint covers

50

^2

per gallon. How many gallons cover its lateral surface? (Use

\pi \approx 3.14

Example 14

medium

A cylinder has total surface area

54\pi

and radius 3. Find its height.

Find height h given r = 3, SA = 54π

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

2

and length

15

. Find its surface area in terms of

\pi

(lateral only).

Example 17

hard

A cylinder's height equals its diameter. If the total surface area is

108\pi

cm², find the radius.

Example 18

medium

A cylinder has lateral surface area

48\pi

and height 6. Find its radius.

Find radius r given h = 6, lateral SA = 48π

Example 19

hard

A cylindrical tube (open both ends) has outer radius

6

, inner radius

5

, length

12

. Find the total surface area in terms of

\pi

Example 20

hard

A cylinder has total surface area

24\pi

. If

r = 1

, find

h

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Related Concepts

Area of a Circle Surface Area Circumference Surface Area of a Cylinder Geometric Modeling