Cylinder Area Calculation: formulas and exercises

THE cylinder area corresponds to the surface measurement of this figure.

Remember that the cylinder is an elongated, rounded spatial geometric figure.

It has two circles with radii of equivalent measure, which are situated in parallel planes.

Note that along the entire length of the cylinder, the diameter measurement will always be the same.

Area Formulas

In the cylinder it is possible to calculate different areas:

Base area (A_B): this figure is formed by two bases: one upper and one lower;
Side area (A_there): corresponds to the measure of the lateral surface of the figure;
Total area (A_t): is the total measure of the figure's surface.

Having made that observation, let's see below the formulas to calculate each one of them:

Base Area

THE_B= π.r²

Where:

THE_B: base area
π (Pi): value constant 3.14
r: lightning

Side Area

THE_there = 2 π.r.h

Where:

THE_there: side area
π (Pi): value constant 3.14
r: lightning
H: height

Total area

At = 2.Ab+Al
or
At = 2(π.r²) + 2(π.r.h)

Where:

THE_t: total area
THE_B: base area
THE_there: side area
π (Pi): value constant 3.14
r: lightning
H: height

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Exercise solved

An equilateral cylinder is 10 cm high. Calculate:

a) the lateral area

See Answer

Note that the height of this cylinder equals twice its radius, so h = 2r. By the formula of the lateral area, we have:

THE_there = 2 π.r.h
THE_there = 2 π.r.2r
THE_there = 4 π.r²
THE_there= 100π cm²

b) the total area

See Answer

Being the base area (A_B) r², we have the formula of the total area:

THE_t= A_there + 2A_B
THE_t = 4 πr²+ 2πr²
THE_t = 6 πr²
THE_t= 150π cm²

Entrance Exam Exercises with Feedback

1. (Cefet-PR) A cylinder of revolution with a base radius of 5 cm is sectioned by a plane parallel to its axis, at a distance of 4 cm from it. If the obtained section area is 12 cm², so the height of the cylinder is equal to:

to 1
b) 2
c) 3
d) 4
e) 5

See Answer

Alternative b: 2

2. (USF-SP) A straight circular cylinder, with a volume of 20π cm³, has a height of 5cm. Its lateral area, in square centimeters, is equal to:

a) 10π
b) 12π
c) 15π
d) 18π
e) 20π

See Answer

Alternative e: 20π

3. (UECE) A straight circular cylinder of 7 cm height has a volume equal to 28π cm³. The total area of this cylinder, in cm², is:

a) 30π
b) 32π
c) 34π
d) 36π

See Answer

Alternative d: 36π

practice with 13 exercises on cylinders.