Volumes of Cylinders



Geometry

Volume of Cylinders and composite figures

Example 1: Find the volume of the following cylinder.

a) Volume = area of the base (circles) x height (perpendicular distance between bases)

b) area of circle = pr2 = (3.14) (8 in)2 = 201 in2

c) V = (201 in2) (18 in) = 3618 in3

8 in

Example 2: Find the volume of the following cylinder.

a) Acircle = pr2 = (3.14) (5 ft)2 = 15.7 ft2

b) V = (15.7 ft2) (25 ft) = 392.5 ft3

Example 3: The volume of a cylinder is 4622.9 cubic inches and has a radius of 9 inches. What is the height of this cylinder?

a) V = (pr2) h

b) 4622.9 in3 = (3.14) (9 in)2 h

c) h = 4622.9 in3 / (3.14) (81 in2) = 18.2 in

Composite shapes- space figures that are a combination of two or more simpler figures. To find the volume of a composite figure, add (or subtract) the volumes of the simpler figures.

Example 4: find the volume

a) Two pieces: the bottom of the house and the roof

b) bottom: V = l w h = (8 in) (14 in) (9 in) = 1008 in3

c) roof: Atriangle = ½bh = ½ (14 in) (5 in) = 35 in2

Vroof = (35 in2) (9 in) = 315 in3

d) Volumehouse = 1008 in3 + 315 in3 = 1323 in3

You try it:

Example 5: find the volume

Break it into two pieces… the answer is 24000 mm3

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Volume of a Cylinder Formula

Volume= Area of Base • Height

18 in

25 ft

10 ft

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