Cylinders
Andrew Gloag
Bill Zahner
Dan Greenberg
Jim Sconyers
Lori Jordan
Victor Cifarelli
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Printed: November 20, 2012
AUTHORS
Andrew Gloag
Bill Zahner
Dan Greenberg
Jim Sconyers
Lori Jordan
Victor Cifarelli
EDITOR
Annamaria Farbizio
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C ONCEPT
Concept 1. Cylinders
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Cylinders
Here you’ll learn what a cylinder is and how to find its volume and surface area.
What if you were given a solid three-dimensional figure with congruent enclosed circular bases that are in parallel
planes? How could you determine how much two-dimensional and three-dimensional space that figure occupies?
After completing this Concept, you’ll be able to find the surface area and volume of a cylinder.
Watch This
MEDIA
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Cylinders CK-12
Guidance
A cylinder is a solid with congruent circular bases that are in parallel planes. The space between the circles is
enclosed.
A cylinder has a radius and a height.
A cylinder can also be oblique (slanted) like the one below.
Surface Area
Surface area is the sum of the area of the faces of a solid. The basic unit of area is the square unit.
Surface Area of a Right Cylinder: SA = 2πr2 + 2πrh.
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2πr
2πr h
| {z } + |{z}
area of
both
circles
length
of
rectangle
To see an animation of the surface area, click http://www.rkm.com.au/ANIMATIONS/animation-Cylinder-SurfaceArea-Derivation.html, by Russell Knightley.
Volume
To find the volume of any solid you must figure out how much space it occupies. The basic unit of volume is the
cubic unit. For cylinders, volume is the area of the circular base times the height.
Volume of a Cylinder: V = πr2 h.
If an oblique cylinder has the same base area and height as another cylinder, then it will have the same volume. This
is due to Cavalieri’s Principle, which states that if two solids have the same height and the same cross-sectional
area at every level, then they will have the same volume.
Example A
Find the surface area of the cylinder.
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Concept 1. Cylinders
r = 4 and h = 12.
SA = 2π(4)2 + 2π(4)(12)
= 32π + 96π
= 128π units2
Example B
The circumference of the base of a cylinder is 16π and the height is 21. Find the surface area of the cylinder.
We need to solve for the radius, using the circumference.
2πr = 16π
r=8
Now, we can find the surface area.
SA = 2π(8)2 + (16π)(21)
= 128π + 336π
= 464π units2
Example C
Find the volume of the cylinder.
If the diameter is 16, then the radius is 8.
V = π82 (21) = 1344π units3
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Cylinders CK-12
Guided Practice
1. Find the volume of the cylinder.
2. If the volume of a cylinder is 484π in3 and the height is 4 in, what is the radius?
3. The circumference of the base of a cylinder is 80π cm and the height is 36 cm. Find the total surface area.
Answers:
1. V = π62 (15) = 540π units3
2. Solve for r.
484π = πr2 (4)
121 = r2
11in = r
3. We need to solve for the radius, using the circumference.
2πr = 80π
r = 40
Now, we can find the surface area.
SA = 2π(40)2 + (80π)(36)
= 3200π + 2880π
= 6080π units2
Practice
1. Two cylinders have the same surface area. Do they have the same volume? How do you know?
2. A cylinder has r = h and the radius is 4 cm. What is the volume?
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Concept 1. Cylinders
3. A cylinder has a volume of 486π f t.3 . If the height is 6 ft., what is the diameter?
4. A right cylinder has a 7 cm radius and a height of 18 cm. Find the volume.
Find the volume of the following solids. Round your answers to the nearest hundredth.
5.
6.
Find the value of x, given the volume.
7. V = 6144π units3
8. The area of the base of a cylinder is 49π in2 and the height is 6 in. Find the volume.
9. The circumference of the base of a cylinder is 34π cm and the height is 20 cm. Find the total surface area.
10. The lateral surface area of a cylinder is 30π m2 and the height is 5m. What is the radius?
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