Transcript Notes 9.4

9.4
V = Bh
Where B = area of the base
And h = height
Example 1
Find the Volume of a Rectangular Prism
Find the volume of the box by determining
how many unit cubes fit in the box.
SOLUTION
The base is 5 units by 3 units. So, 3 · 5,
or 15 unit cubes are needed to cover
the base layer.
There are 4 layers. Each layer has
15 cubes. So, the total number of
cubes is 4 · 15, or 60.
ANSWER
The volume of the box is 60 cubic units.
Example 2
Find the Volume of a Prism
Find the volume of the prism.
b.
a.
SOLUTION
a. V = Bh
Write the formula for volume of a prism.
= (7 · 4) · 5
= 140
ANSWER
Area of rectangular base = l · w = 7 · 4.
Simplify.
The volume is 140 cubic inches.
Example 2
Find the Volume of a Prism
b. V = Bh
Write the formula for volume of a prism.
1–
= 2·8·6 ·3
Area of triangular base = – · 8 · 6.
= 72
Simplify.
ANSWER
1
2
The volume is 72 cubic feet.
Checkpoint
Find Volume of Prisms
Find the volume of the prism.
1.
3.
2.
Checkpoint
Find Volume of Prisms
Find the volume of the prism.
1.
ANSWER
216 ft3
ANSWER
125 cm3
ANSWER
245 in.3
2.
3.
V=
2
πr h
Example 3
Compare Volumes of Cylinders
a. How do the radius and height of
the mug compare to the radius
and height of the dog bowl?
b. How many times greater is the
volume of the bowl than the
volume of the mug?
SOLUTION
a. The radius of the mug is 2 inches and the radius of
the dog bowl is 6 inches. The radius of the bowl is
three times the radius of the mug. The height of the
mug is the same as the height of the bowl.
Example 3
Compare Volumes of Cylinders
b. Volume of mug
V=
Write the formula for
volume.
πr2h
= π(22)(4)
= 16π
Volume of dog bowl
Substitute for r and for h.
Simplify.
V = πr2h
= π(62)(4)
= 144π
To compare the volume of the bowl to the volume of
the mug, divide the volume of the bowl by the
volume of the mug.
Volume of bowl
144π
–––––––––––––– = ––––– = 9
16π
Volume of mug
ANSWER
The volume of the bowl is nine times the
volume of the mug.
Checkpoint
Find Volume of Cylinders
Find the volume of the cylinder. Round your answer
to the nearest whole number.
4.
6.
5.
Checkpoint
Find Volume of Cylinders
Find the volume of the cylinder. Round your answer
to the nearest whole number.
4.
5.
ANSWER
38 ft3
ANSWER
16 in.3
ANSWER
126 m3
6.
Review
Find the surface area of the solid. If necessary,
round your answer to the nearest whole number.
1.
ANSWER
150 m2
ANSWER
2286 mm2
2.
3. Find the lateral area of a right cone with radius 5
inches and slant height 22 inches. Round your
answer to the nearest whole number.
ANSWER
346 in.2
• Worksheet 9.4A