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.r^{2}
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.r^{2}) + 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
Exercise solved
An equilateral cylinder is 10 cm high. Calculate:
a) the lateral area
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.r^{2}
THE_{there }= 100π cm^{2}
b) the total area
Being the base area (A_{B}) r^{2}, we have the formula of the total area:
THE_{t }= A_{there} + 2A_{B}
THE_{t} = 4 πr^{2 }+ 2πr^{2}
THE_{t} = 6 πr^{2}
THE_{t }= 150π cm^{2}
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 cm^{2}, so the height of the cylinder is equal to:
to 1
b) 2
c) 3
d) 4
e) 5
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
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
Alternative d: 36π
practice with 13 exercises on cylinders.
Read too:
- Cylinder
- Cylinder Volume
- Spatial Geometry
- Math Formulas