Name: ___________________________________
Date: _________________
CYLINDERS
GEOMETRY N
Cylinders are three-dimensional closed surfaces.
In general use, the term cylinder refers to a right circular cylinder with its ends closed to form two circular
surfaces, which lie in parallel planes. Also, the lateral surface is perpendicular to the bases.
Height
Radius of Base
Finding the Lateral Surface Area of a Cylinder
A typical view of the lateral surface is the label on a can which, when removed and flattened out, forms a
rectangle. Therefore, to calculate the lateral surface area we have to find the circumference of the base, which
represents the length of the rectangle, and multiply it by the height.
Lateral Surface Area of a Cylinder
LA  circumference  height
or
LA  (2r )  h
Exercise #1: Find the lateral surface area of a right circular cylinder that has a radius of 5 inches and a height
of 10 inches. Leave your answer in terms of π.
Finding the Total Surface Area of a Cylinder
To find the total surface area of a cylinder we have to find the lateral area and add the area of the 2 bases, which
are circles.
Total Surface Area of a Cylinder
Surface Area  LA  2  area of bases
or
Surface Area  2 rh  2 r 2
Surface Area = LA + 2*bases
Exercise #2: Find the total surface area of a right circular cylinder that has a height of 12 inches and a diameter
or
of 10 inches. Leave your answer in terms of π.
Surface Area =
Exercise #3: Find the total surface area of a right circular cylinder that has a height of 7 millimeters and a
radius of 8 millimeters. Round your answer to the nearest hundredth.
Exercise #4: If the lateral area for a right circular cylinder is 30 sq. ft. and the height is 5 ft. , find the radius
of the base.
For 5 – 7: In the following right circular cylinder problems, let h = altitude, d = diameter, and r = radius. Leave
the answers in terms of  . For each cylinder, find (a) the lateral surface area, and (b) the total surface area.
5. r  3.5 cm. and h  16 cm.
Lateral Area: _____________
Surface Area: _____________
6. d = 12 in and h  8 in.
Lateral Area: _____________
Surface Area: _____________
7. r  2 in. and h  4 in.
Lateral Area: _____________
Surface Area: _____________