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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. 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
Finding the volume of a Finding the volume of a PrismPrism►PrismPrism – 2 – 2 parallel bases and faces parallel bases and faces
are rectangles. Cross sections are are rectangles. Cross sections are congruent to the bases. What is a congruent to the bases. What is a Cross section?
Height (h)
Area of Base (B)
V = BhHeight of PrismArea of Base or
Cross Section
A = lw (Rectangle)
Finding the Volume of a 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?
Find the Volume of the PrismFind the Volume of the Prism
5in3in
10inV = Bh
= (3in • 5in)(10in)
= (15in2)(10in)
= 150in3
Area of Base
B = l•w
Discussion: What prism is this? Discussion: What prism is this? Look at the Look at the Cross Section to to determine. Why can’t you use l • determine. Why can’t you use l • w • h?w • h?
8in
10inV = Bh
= ½bh • h
= ½(8in) __ • (10in)
= (12in2) • (10in)
= 120in3
3in
3 in
Now work on this prism! It’s tricky so Now work on this prism! It’s tricky so be careful.be careful.
20m
29m
40m
V = Bh
= ½bh • h
= ½(20m)__ • (40m)
= 210m2 • 40m
= 8400m3Height of the base:
a
a2 + b2 = c2
a2 + 202 = 292
a = 21
Triangle
21
Volume of a CylinderVolume of a CylinderVideo for help: Video for help: YouTube
r
h
V = Bh
Volume of right cylinder
Height of cylinder
Area of base or cross section: (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
= 3.14(8ft)2 • (9ft)
= 200.96ft2 • (9ft)
= 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
12in4in
11in
Volume of Prism:
Vp = Bh
= (11)(12)(4)
= 528in3
VT = Vc + Vp
= 226in3 + 528in3
= 754in3
What have we learned??What have we learned??Volume of a prism or a cylinder:
V = Bh
Capitol “B” stands for area of the base.
Composite Figures: Made up of two separate solids.
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