Transcript Volume of a Prism/Cylinder PowerPoint - 126 Math

Volumes of Prisms & Cylinders
Objectives:
1) To find the volume of a prism.
2) To find the volume of a cylinder.
Volume
► Volume
occupies.
– Is the space that a figure
 Measured in cubic units.
►cm3,
in3, m3, ft3
Finding the volume of a Prism
– 2  parallel bases and faces are
rectangles. Cross sections are congruent
to the bases. What is a Cross section?
► Prism
V = Bh
Height (h)
Area of Base or
Cross Section
A = lw (Rectangle)
Area of
Base (B)
Height of
Prism
Finding the Volume of a rectangular
prism
► The
box shown is 5
units long, 3 units
wide, and 4 units high.
How many unit cubes
will fit in the box?
What is the volume of
the box?
Find the Volume of the Prism
Area of Base
B = l•w
V = Bh
10in
= (3in • 5in)(10in)
= (15in2)(10in)
3in
5in
= 150in3
Discussion: What prism is this? Look at
the Cross Section to determine. Why
can’t you use l • w • h?
3 in
8in
10in
V = Bh
= ½bh • h
= ½(8in) 3in
__ • (10in)
= (12in2) • (10in)
= 120in3
Now work on this prism! It’s tricky so be
careful.
Triangle
29m
V = Bh
= ½bh • h
a
20m
Height of the base:
a2 + b 2 = c 2
a2 + 202 = 292
a = 21
40m
21 • (40m)
= ½(20m)__
= 210m2 • 40m
= 8400m3
Volume of a Cylinder
Video for help: YouTube
r
Height of
cylinder
V = Bh
h
Volume of
right cylinder
Area of base or
cross section:
(Circle)
A = r2
Ex.4: Find the area of the following right cylinder.
Area of a Circle
V = Bh
= r2 • h
16ft
= 3.14(8ft)2 • (9ft)
9ft
= 200.96ft2 • (9ft)
= 1809.6ft3
Ex.5: Find the volume of the following
composite figure.
Half of a cylinder:
Vc = Bh
= r2•h
= (6in)2 • (4in)
= 452in3
11in
4in
= 452/2 = 226in3
12in
VT = Vc + Vp
Volume of Prism:
= 226in3 + 528in3
= (11)(12)(4)
= 754in3
= 528in3
Vp = Bh
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.