1. This is a rectangular prism (box), therefore its volume is written as V = w l h where w is the width, l is the length, and h is the height.
w = 2 1/4 (2.25) m
l = 3 m
h = 8 1/4 (8.25) m
V = w l h
V = 2.25×3×8.25
V = 55.69 m³
2. This is a cube, as shown by the measurements all being equal. Its volume is written as V = a³ where a is the length of any side.
a = 3 1/4 (3.25) in
V = a³
V = 3.25³
V = 33.33 in³
# 3 through 8 are all rectangular prisms (boxes), whose volume is written as V = w l h
3.
w = 2 1/3 (2.33) ft
l = 9 1/4 (9.25) ft
h = 4 ft
V = w l h
V = 2.33×9.25×4
V = 86.21 ft³
4.
w = 3.7 in
l = 10.3 in
h = 2.4 in
V = w l h
V = 3.7×10.3×2.4
V = 91.46 in³
5.
w = 4 in
l = 7 in
h = 5 in
V = w l h
V = 4×7×5
V = 140 in³
6.
w = 5 in
l = 3.6 in
h = 4.2 in
V = w l h
V = 5×3.6×4.2
V = 75.6 in³
7.
w = 2.2 cm
l = 6.6 cm
h = 3 cm
V = w l h
V = 2.2×6.6×3
V = 43.56 cm³
8.
w = 2.1 m
l = 4.2 m
h = 12.2 m
V = w l h
V = 2.1×4.2×12.2
V = 107.60 m³
9. This is a cube again, therefore its volume is written as V = a² where a is the length of any side.
a = 2.3 ft
V = a³
V = 2.3³
V = 12.17 ft³
10. A rectangular box (prism) 12.7 cm long, 7.1 cm wide, and 3 cm high.
V = w l h
V = 7.1×12.7×3
V = 270.51 cubic cm (cm³)
11. A cube 11 1/4 (11.25) inches long.
V = a³
V = 11.25³
V = 1423.83 cubic inches (in³)
12. A rectangular box (prism) 9.8 feet long, 4 feet wide, and 2 1/2 (2.5) feet high.
V = w l h
V = 4×9.8×2.5
V = 98 cubic feet (ft³)
Use the formula V=bh or V=l×w×h (V = w l h) to find the volume of each.
1. Area of base: 8 × 3 = 24 square units
Height: 4 1/2 (4.25) units
V = bh
V = 24×4.25
V = 102 cubic units
2. V = l×w×h
V = bh
V = 3.6×5×4.2
V = 75.6 cubic inches
3. V = bh
b = lw
l = 4 ft
w = 2 1/2 (2.5) ft
b = 4×2.5
b = 10
h = 7
V = bh
V = 10×7
V = 70 cubic feet
4. A rectangular box 6.8 feet long, 4 feet wide, and 2 feet high.
(is it just me, or does that one sound like the dimensions of a coffin???)
V = l×w×h
V = 6.8×4×2
V = 54.4 cubic feet
5. A cube 3 1/2 (3.5) inches long. Draw a picture and label it. Tell how it can help you find the volume.
V = bh
b = l×w
b = 3.5×3.5
b = 12.25
h = 3.5
V = 12.25×3.5
V = 42.88 cubic inches
Drawing attached.
