cubic meters.
8-8 Volume and Surface Area of Composite Figures
3
2.3 m
Find the volume of the composite figure. Round
to the nearest tenth if necessary.
The figure is made up of a triangular prism and a
rectangular prism.
Volume of triangular prism
The figure is made up of two pyramids.
Volume of top pyramid
Volume of bottom pyramid
Volume of rectangular prism
3
3
3
0.693 m + 1.584 m = 2.277 m
The volume of the composite figure is about 2.3
cubic meters.
3
2.3 m
3
3
3
5 m + 8 m = 13 m
The volume of the composite figure is 13 cubic
meters.
13 m
3
Find the surface area of the composite figure.
Round to the nearest tenth if necessary.
The figure is made up of two pyramids.
Volume of top pyramid
The figure is made up of a cube and a square
pyramid.
Surface area of bottom cube minus area where the
two prisms connect
Volume of bottom pyramid
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Lateral surface area of top square pyramid
Page 1
The volume of the composite figure is 13 cubic
meters.
2
The surface area of the composite figure is 2,600 ft .
8-8 Volume and Surface Area of Composite Figures
3
13 m
2,600 ft
2
Find the surface area of the composite figure.
Round to the nearest tenth if necessary.
The figure is made up of two rectangular prisms.
Surface area of bottom rectangular prism minus area
of bottom surface of top rectangular prism
The figure is made up of a cube and a square
pyramid.
Surface area of bottom cube minus area where the
two prisms connect
Surface area of top rectangular prism minus area of
bottom surface
Lateral surface area of top square pyramid
2
2
2
570 m + 150 m = 720 m
2
The surface area of the composite figure is 720 m .
2
The lateral area of the square pyramid is 600 ft .
2
2
2
2,000 ft + 600 ft = 2,600 ft
2
720 m
2
The surface area of the composite figure is 2,600 ft .
2,600 ft
Find the volume of the figure shown in cubic feet.
Round to the nearest tenth.
2
The figure is made up of a triangular prism and a
rectangular prism. Convert all measurements to feet.
12 in. = 1 ft
The figure is made up of two rectangular prisms.
Surface area of bottom rectangular prism minus area
of bottom surface of top rectangular prism
5 in. =
ft
10 in. =
ft
24 in. = 2 ft
Surface area of top rectangular prism minus area of
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bottom
surface
Volume of triangular prism
Page 2
570 m + 150 m = 720 m
2
The surface area of the composite figure is 720 m .
8-8 Volume and Surface Area of Composite Figures
2
720 m
Find the volume of the figure shown in cubic feet.
Round to the nearest tenth.
The volume of the composite figure is about 0.5
cubic feet.
0.5 ft
3
Reason Inductively The swimming pool shown is
being filled with water. Find the number of cubic feet
that it will take to fill the swimming pool. (Hint: The
area of a trapezoid is
The figure is made up of a triangular prism and a
rectangular prism. Convert all measurements to feet.
12 in. = 1 ft
5 in. =
ft
10 in. =
ft
24 in. = 2 ft
.)
The swimming pool is made up of a rectangular
prism and a trapezoidal prism.
Volume of rectangular prism
Volume of triangular prism
Volume of the trapezoidal prism. The bases are 8 ft
and 3 feet, and the height is 30 14 or 16 ft.
Volume of rectangular prism
1,344 ft + 1,056 ft = 2,400 ft
3
3
3
3
The volume of the swimming pool is 2,400 ft .
2,400 ft
3
3
3
0.2 ft + 0.3 ft = 0.5 ft
The volume of the composite figure is about 0.5
cubic feet.
0.5 ft
3
Copy and Solve Show your work on a separate
piece of paper. Round to the nearest tenth.
Find the surface area of the figure shown.
3
Reason Inductively The swimming pool shown is
being filled with water. Find the number of cubic feet
that it will take to fill the swimming pool. (Hint: The
area of a trapezoid is
.)
The figure is made up of a rectangular prism and a
triangular prism.
Surface area of bottom rectangular prism minus the
area where the two prisms connect
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The swimming pool is made up of a rectangular
Page 3
Surface area of top triangular prism but not the area
where the two prisms connect
1,344 ft + 1,056 ft = 2,400 ft
2
The surface area of the composite figure is 10.4 m .
3
The volume of the swimming pool is 2,400 ft .
8-8 Volume and Surface Area of Composite Figures
3
2,400 ft
Copy and Solve Show your work on a separate
piece of paper. Round to the nearest tenth.
Find the surface area of the figure shown.
The figure is made up of a rectangular prism and a
triangular prism.
Surface area of bottom rectangular prism minus the
area where the two prisms connect
10.4 m
2
Find the volume of the figure shown.
The figure is made up of two rectangular prisms.
Volume of top rectangular prism
Volume of bottom rectangular prism
Surface area of top triangular prism but not the area
where the two prisms connect
The area of each triangle is
or 0.63.
The area of the first rectangle is 1.1 1.14 or 1.254.
The area of the second rectangle is 1.1 1.14 or
1.254.
The sum of the areas of the sides is 0.63 + 0.63 +
3
3
3
108 m + 864 m = 972 m
The volume of the composite figure is 972 cubic
meters.
2
1.254 + 1.254 or 3.8 m .
2
2
6.6 m + 3.8 m = 10.4 m
3
972 m
2
2
The surface area of the composite figure is 10.4 m .
10.4 m
A carryout container is shown. The bottom base is a
4-inch square and the top base is a 4-inch by 6-inch
rectangle. The height of the container is 5 inches.
Find the volume of food that it holds.
2
Find the volume of the figure shown.
The figure is made up of two rectangular prisms.
Volume of top rectangular prism
The food container is made up of a rectangular prism
and two triangular prisms.
Volume of the rectangular prism
Page 4
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Volume of triangular prisms
Volume of bottom rectangular prism
The volume of the composite figure is 972 cubic
meters.
8-8 Volume and Surface Area of Composite Figures
3
972 m
Volume:
The house is made up of a triangular prism and a
rectangular prism.
Volume of triangular prism
A carryout container is shown. The bottom base is a
4-inch square and the top base is a 4-inch by 6-inch
rectangle. The height of the container is 5 inches.
Find the volume of food that it holds.
Volume of rectangular prism
3
3
3
300 m + 1,080 m = 1,380 m
The volume of the house is 1,380 cubic meters.
The food container is made up of a rectangular prism
and two triangular prisms.
Volume of the rectangular prism
Volume of triangular prisms
3
3
3
80 in + 20 in = 100 in
3
Surface area:
The house is made up of a rectangular prism and a
triangular prism.
Surface area of bottom rectangular prism minus the
top and bottom of the prism
Surface area of top triangular prism but not the area
where the two prisms connect
The area of each triangle is
or 25.
The area of the first rectangle is 7.1 12 or 85.2.
The area of the second rectangle is 7.1 12 or 85.2.
The sum of the areas of the sides is 25 + 25 + 85.2 +
2
85.2 or 220.4 m .
2
2
2
396 m + 220.4 m = 616.4 m
2
The surface area of the house is 616.4 m .
100 in
Refer to the house shown. Find the surface area and
volume of the house. Do not include the bottom of
the house when calculating the surface area.
3
volume: 1,380 m ; surface area: 616.4 m
2
Jaime is covering the boxes shown in felt, including
the back and bottom. What is the total area to be
covered with felt?
Volume:
The house is made up of a triangular prism and a
rectangular prism.
Volume of triangular prism
A. 23 in2
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2
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B. 117 in
C. 172 in2
2
396 m + 220.4 m = 616.4 m
2
The surface area of the house is 616.4 m .
8-8 Volume and Surface Area of Composite Figures
3
2
volume: 1,380 m ; surface area: 616.4 m
Jaime is covering the boxes shown in felt, including
the back and bottom. What is the total area to be
covered with felt?
A. 23 in2
2
B. 117 in
C. 172 in2
2
D. 1,260 in
The figure is made up of two rectangular prisms.
Surface area of bottom rectangular prism minus area
of bottom surface of top rectangular prism
Surface area of top rectangular prism minus area of
bottom surface
2
2
138 in + 34 in = 172 in
2
2
The total area to be covered is 172 in . The answer
is C.
C
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