NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 8 Reteach
Volume and Surface Area of Composite Figures
Example 1
Find the surface area of the composite figure.
To find the surface area, find the sum of the areas of
exposed surfaces. The lateral area of the prism is 50 +
10 + 50 + 10 = 120 m2. The area of the bottom of the
prism is 10 × 2 = 20 m2. The surface area of the
triangular prism is 2 + 2 + 28 + 20 = 52 m2. So, the
surface area is 120 + 20 + 52 = 192 m2.
2m
2.8 m
5m
2m
10 m
Example 2
Find the volume of the composite figure.
0.5 m
0.5 m
1m
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
1m
2m
The figure is made up of two rectangular prisms.
V = ℓwh + ℓwh
V = 2 · 1 · 1 + 2 · 0.5 · 0.5
V = 2 + 0.5 or 2.5
The volume of the composite figure is 2.5 cubic meters.
Exercises
1. Find the volume of the composite figure. 2. Find the surface area of the composite
figure.
2 in.
3 in.
1 ft
2 ft
7 in.
4 ft
9 ft
12 in.
2 in.
2 in.
Course 2 • Chapter 8 Measure Figures
4 ft
16 ft
135
NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 8 Skills Practice
Volume and Surface Area of Composite Figures
Find the volume and surface area of each composite figure.
1.
2.
10 m
3.
4 mm
3 mm
1 cm
2.5 cm
1 cm
9 mm
6m
4m
2.3 cm
5m
5 cm
20 mm
16 m
9 mm
12 mm
Find the volume of each composite figure.
6 ft
4.
5.
6. 3 mm
4 in.
10 ft
3 in.
10 mm
8 mm
20 ft
9 in.
11 mm
7. MULCH Marcus is putting a border of mulch around a tree. The figure
shows the top view of the mulch. The mulch will be 3 inches deep.
Find the volume of mulch.
20 in.
24 in.
136
Course 2 • Chapter 8 Measure Figures
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
10 ft
NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 8 Homework Practice
Volume and Surface Area of Composite Figures
Find the volume of each composite figure.
2.
1.
2 ft
3.
6 cm
0.5 cm
5 cm
5m
5m
13 m
0.5 cm
4 ft
6 cm
1.5 ft
4m
0.5 cm
5 cm
6 cm
2 ft
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
4. TABLE Rina is building a table as shown in the figure.
Find the volume of wood she needs for the table. The
table legs are 24 inches tall with a length and width
of 2 inches.
30 in.
1 in.
20 in.
Find the surface area of each composite figure.
5.
6.
7 cm
3.6 cm
3.6 ft
2 cm
3 cm
3.6 ft
area of base
5.6 ft2
2 ft
6 cm
3 cm
6 cm
7.
8 cm
3.6 ft
12 cm
2 cm
4 cm
Course 2 • Chapter 8 Measure Figures
3.6 cm
4 ft
135
NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 8 Reteach
Volume and Surface Area of Composite Figures
Example 1
Find the surface area of the composite figure.
To find the surface area, find the sum of the areas of
exposed surfaces. The lateral area of the prism is 50 +
10 + 50 + 10 = 120 m2. The area of the bottom of the
prism is 10 × 2 = 20 m2. The surface area of the
triangular prism is 2 + 2 + 28 + 20 = 52 m2. So, the
surface area is 120 + 20 + 52 = 192 m2.
2m
2.8 m
5m
2m
10 m
Example 2
Find the volume of the composite figure.
0.5 m
0.5 m
1m
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
1m
2m
The figure is made up of two rectangular prisms.
V = ℓwh + ℓwh
V = 2 · 1 · 1 + 2 · 0.5 · 0.5
V = 2 + 0.5 or 2.5
The volume of the composite figure is 2.5 cubic meters.
Exercises
1. Find the volume of the composite figure. 2. Find the surface area of the composite
figure.
2 in.
3 in.
1 ft
2 ft
7 in.
4 ft
9 ft
12 in.
2 in.
4 ft
2 in.
100 in3
Course 2 • Chapter 8 Measure Figures
16 ft
512 ft2
135
NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 8 Skills Practice
Volume and Surface Area of Composite Figures
Find the volume and surface area of each composite figure.
1.
2.
10 m
3.
4 mm
3 mm
1 cm
2.5 cm
1 cm
9 mm
6m
4m
2.3 cm
5m
5 cm
20 mm
16 m
9 mm
12 mm
560 m3; 444 m2
2,268 mm3;
1,182 mm2
17.25 cm3;
45.9 cm2
Find the volume of each composite figure.
6 ft
4.
5.
6. 3 mm
4 in.
10 ft
3 in.
10 mm
8 mm
20 ft
2,400 ft3
9 in.
39 in3
11 mm
1,012 mm3
7. MULCH Marcus is putting a border of mulch around a tree. The figure
shows the top view of the mulch. The mulch will be 3 inches deep.
Find the volume of mulch. 528 in3
20 in.
24 in.
136
Course 2 • Chapter 8 Measure Figures
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
10 ft
NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 8 Homework Practice
Volume and Surface Area of Composite Figures
Find the volume of each composite figure.
2.
1.
2 ft
3.
6 cm
0.5 cm
5 cm
5m
5m
13 m
0.5 cm
4 ft
6 cm
1.5 ft
4m
0.5 cm
5 cm
6 cm
2 ft
14 ft3
31.5 cm3
375 m3
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
4. TABLE Rina is building a table as shown in the figure.
Find the volume of wood she needs for the table. The
table legs are 24 inches tall with a length and width
of 2 inches. 984 in3
30 in.
1 in.
20 in.
Find the surface area of each composite figure.
5.
6.
7 cm
3.6 cm
3.6 ft
2 cm
3 cm
3.6 ft
area of base
5.6 ft2
2 ft
6 cm
3 cm
6 cm
7.
8 cm
3.6 ft
12 cm
2 cm
4 cm
233.6
314 cm2
Course 2 • Chapter 8 Measure Figures
4 ft
3.6 cm
233.6 cm2
84.8 ft2
135