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Volumes of Prisms & Cylinders. Objectives: 1) To find the volume of a prism. 2) To find the volume of a cylinder. Volume. Volume – Is the space that a figure occupies. Measured in cubic units. cm 3 , in 3 , m 3 , ft 3. I. Finding the volume of a Prism. - PowerPoint PPT Presentation
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Volumes of Prisms & Volumes of Prisms &
CylindersCylinders
Objectives:Objectives:
1) To find the volume of a prism.1) To find the volume of a prism.
2) To find the volume of a cylinder.2) To find the volume of a cylinder.
VolumeVolume
►VolumeVolume – Is the space that a figure – Is the space that a figure occupies.occupies. Measured in cubic units.Measured in cubic units.
►cmcm33, in, in33, m, m33, ft, ft33
I. Finding the volume of a I. Finding the volume of a PrismPrism►PrismPrism – 2 – 2 parallel bases, sides parallel bases, sides
(Lats) are rectangles.(Lats) are rectangles.
Height (h)
Area of Base (B)
V = BhHeight of PrismArea of Base
A = bh (Rectangle)
A = ½bh (Triangle)
Ex. 1: Finding the Volume of a Ex. 1: Finding the Volume of a rectangular prismrectangular prism
► The box shown is 5 The box shown is 5 units long, 3 units units long, 3 units wide, and 4 units wide, and 4 units high. How many high. How many unit cubes will fit in unit cubes will fit in the box? What is the box? What is the volume of the the volume of the box?box?
Ex.1: Find the Volume of the Ex.1: Find the Volume of the PrismPrism
5in
3in
10inV = Bh
= (3in • 5in)(10in)
= (15in2)(10in)
= 150in3
Area of Base
B = l•w
Ex.2: Find the volume of the followingEx.2: Find the volume of the following
20m
29m
40m
V = Bh
= ½bh • h
= ½(20m)__ • (40m)
= 210m2 • 40m
= 8400m3
21
Triangle
21
Ex.3: Yet another prism! Find Ex.3: Yet another prism! Find the the volume.volume.
8in
10in
V = Bh
= ½bh • h
= ½(8in) __ • (10in)
= (27.7in2) • (10in)
= 277in3
h=6.9
6.9
II. Volume of a CylinderII. Volume of a Cylinder
r
h
V = Bh
Volume of right cylinder
Height of cylinder
Area of base: (Circle)
A = r2
Ex.4: Find the area of the following right Ex.4: Find the area of the following right cylinder.cylinder.
16ft
9ft
V = Bh
= r2 • h
= (8ft)2 • (9ft)
= 64ft2 • (9ft)
= 576ft3
= 1809.6ft3
Area of a Circle
Ex.5: Find the volume of the Ex.5: Find the volume of the following composite figure.following composite figure.
Half of a cylinder:
Vc = Bh
= r2•h
= (6in)2 • (4in)
= 452in3
452/2 = 226in3
12in
4in
11in
Volume of Prism:
Vp = Bh
= (11)(12)(4)
= 528in3
VT = Vc + Vp
= 226in3 + 528in3
= 754in3
