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.
