Name
Reteaching
18-4
Volume of Triangular Prisms
and Cylinders
For any prism, V ! (Area of base) # (height of prism)
Find the volume of the triangular prism.
Base: height ! 2 cm
base ! 3 cm
Height of prism: 8 cm
Step 1: Find the area of the base.
B ! "r2
B ! 3.14 # 32
B ! 28.26 sq in.
Step 1: Find the area of the base:
B ! _12 (b # h)
B ! _12 (2 # 3)
B ! 3 cm2
Step 2: Multiply by the height of the cylinder.
V!B#h
V ! 28.26 # 5
V ! 141.3 cu in.
Step 2: Multiply by the height of the prism.
V!B#h
V!3#8
V ! 24 cm3
Reteaching 18-4
Find the volume of the cylinder:
Radius of base ! 3 in.
Height of cylinder ! 5 in.
Find the volume of each solid.
9 in.
1.
8 cm
2.
3 cm
6 in.
5 in.
3.
4.
1.5 in.
9 ft
© Pearson Education, Inc. 6
9 ft
20 ft
5.2 in.
5. Reasoning If a triangular prism (base of triangle ! 5 in., height of
triangle ! 6 in., height of prism ! 10 in.) is placed inside a cylinder
(radius ! 4 in., height ! 15 in.), how much space will be left over
inside the cylinder?
Topic 18
41
Name
Reteaching
18-4
Volume of Triangular Prisms
and Cylinders
For any prism, V ! (Area of base) # (height of prism)
Find the volume of the triangular prism.
Base: height ! 2 cm
base ! 3 cm
Height of prism: 8 cm
Step 1: Find the area of the base.
B ! "r2
B ! 3.14 # 32
B ! 28.26 sq in.
Step 1: Find the area of the base:
B ! _12(b # h)
B ! _12 (2 # 3)
B ! 3 cm2
Step 2: Multiply by the height of the cylinder.
V!B#h
V ! 28.26 # 5
V ! 141.3 cu in.
Step 2: Multiply by the height of the prism.
V!B#h
V!3#8
V ! 24 cm3
Reteaching 18-4
Find the volume of the cylinder:
Radius of base ! 3 in.
Height of cylinder ! 5 in.
Find the volume of each solid.
9 in.
1.
8 cm
2.
3 cm
6 in.
5 in.
V ! 602.88 cm3
V ! 135 cu in.
3.
4.
1.5 in.
9 ft
9 ft
20 ft
© Pearson Education, Inc. 6
V ! 810 cu ft
5.2 in.
V ! 36.738 cu in.
5. Reasoning If a triangular prism (base of triangle ! 5 in., height of
triangle ! 6 in., height of prism ! 10 in.) is placed inside a cylinder
(radius ! 4 in., height ! 15 in.), how much space will be left over
inside the cylinder?
Prism volume ! 150 cu in.,
cylinder volume ! 753.6 cu in.,
difference in volume ! 753.6 " 150 ! 603.6 cu in.
Topic 18
41