Decide whether each equation is true for all, one, or no values of x.
1 answer:
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1. This is a rectangular prism (box), therefore its volume is written as V = <em>w l h</em> where <em>w</em> is the width, <em>l</em> is the length, and <em>h </em>is the height.
<em>w</em> = 2 1/4 (2.25) m
<em>l</em> = 3 m
<em>h</em> = 8 1/4 (8.25) m
V = <em>w l h</em>
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 = <em>a</em><em>³</em> where <em>a</em> is the length of any side.
<em>a</em> = 3 1/4 (3.25) in
V = <em>a</em><em>³</em>
V = 3.25³
V = 33.33 in³
# 3 through 8 are all rectangular prisms (boxes), whose volume is written as V = <em>w l h</em>
3.
<em>w </em>= 2 1/3 (2.33) ft
<em>l </em>= 9 1/4 (9.25) ft
<em>h</em> = 4 ft
V = <em>w l h</em>
V = 2.33×9.25×4
V = 86.21 ft³
4.
<em>w </em>= 3.7 in
<em>l</em> = 10.3 in<em>
h</em><em> </em>= 2.4 in<em>
</em>V = <em>w l h</em>
V = 3.7×10.3×2.4
V = 91.46 in³
5.
<em>w</em> = 4 in
<em>l</em> = 7 in
<em>h</em> = 5 in
V = <em>w l h</em>
V = 4×7×5
V = 140 in³
6.
<em>w</em> = 5 in
<em>l</em> = 3.6 in
<em>h</em> = 4.2 in
V = <em>w l h</em>
V = 5×3.6×4.2
V = 75.6 in³
7.
<em>w</em> = 2.2 cm
<em>l</em> = 6.6 cm
<em>h</em> = 3 cm
V = <em>w l h</em>
V = 2.2×6.6×3
V = 43.56 cm³
8.
<em>w</em> = 2.1 m
<em>l</em> = 4.2 m
<em>h</em> = 12.2 m
V = <em>w l h</em>
V = 2.1×4.2×12.2
V = 107.60 m³
9. This is a cube again, therefore its volume is written as V = <em>a²</em> where <em>a</em> is the length of any side.
<em>a</em> = 2.3 ft
V = <em>a³</em>
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 = <em>w l h</em>
V = 7.1×12.7×3
V = 270.51 cubic cm (cm³)
11. A cube 11 1/4 (11.25) inches long.
V = <em>a³</em>
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 = <em>w l h</em>
V = 4×9.8×2.5
V = 98 cubic feet (ft³)
Use the formula V=bh or V=l×w×h (V = <em>w l h) </em>to find the volume of each.
1. Area of base: 8 × 3 = <u /><u />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.
<em>w</em> = 2 1/4 (2.25) m
<em>l</em> = 3 m
<em>h</em> = 8 1/4 (8.25) m
V = <em>w l h</em>
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 = <em>a</em><em>³</em> where <em>a</em> is the length of any side.
<em>a</em> = 3 1/4 (3.25) in
V = <em>a</em><em>³</em>
V = 3.25³
V = 33.33 in³
# 3 through 8 are all rectangular prisms (boxes), whose volume is written as V = <em>w l h</em>
3.
<em>w </em>= 2 1/3 (2.33) ft
<em>l </em>= 9 1/4 (9.25) ft
<em>h</em> = 4 ft
V = <em>w l h</em>
V = 2.33×9.25×4
V = 86.21 ft³
4.
<em>w </em>= 3.7 in
<em>l</em> = 10.3 in<em>
h</em><em> </em>= 2.4 in<em>
</em>V = <em>w l h</em>
V = 3.7×10.3×2.4
V = 91.46 in³
5.
<em>w</em> = 4 in
<em>l</em> = 7 in
<em>h</em> = 5 in
V = <em>w l h</em>
V = 4×7×5
V = 140 in³
6.
<em>w</em> = 5 in
<em>l</em> = 3.6 in
<em>h</em> = 4.2 in
V = <em>w l h</em>
V = 5×3.6×4.2
V = 75.6 in³
7.
<em>w</em> = 2.2 cm
<em>l</em> = 6.6 cm
<em>h</em> = 3 cm
V = <em>w l h</em>
V = 2.2×6.6×3
V = 43.56 cm³
8.
<em>w</em> = 2.1 m
<em>l</em> = 4.2 m
<em>h</em> = 12.2 m
V = <em>w l h</em>
V = 2.1×4.2×12.2
V = 107.60 m³
9. This is a cube again, therefore its volume is written as V = <em>a²</em> where <em>a</em> is the length of any side.
<em>a</em> = 2.3 ft
V = <em>a³</em>
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 = <em>w l h</em>
V = 7.1×12.7×3
V = 270.51 cubic cm (cm³)
11. A cube 11 1/4 (11.25) inches long.
V = <em>a³</em>
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 = <em>w l h</em>
V = 4×9.8×2.5
V = 98 cubic feet (ft³)
Use the formula V=bh or V=l×w×h (V = <em>w l h) </em>to find the volume of each.
1. Area of base: 8 × 3 = <u /><u />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.