9514 1404 393
Answer:
a) 7.1 cm
b) 2.8 m
c) 8.3 cm
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h
Of course, the volume formula for the trough will be half that:
V = (1/2)πr²h
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a) 2.5 L will be 2.5×1000 cm³ = 2500 cm³.
Solving the volume formula for radius, we have ...
r² = V/(πh)
r = √(V/(πh)) = √(2500/(π·16)) ≈ 7.1 . . . . . cm
The radius of the can is about 7.1 cm.
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b) 20 L will be 20,000 cm³.
Solving the relevant volume formula for height, we have ...
h = 2V/(πr²) = 2(20,000)/(π(13.5/2)²) ≈ 279.4 . . . cm
279.4 cm ≈ 2.8 m
The length of the gutter is about 2.8 m.
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c) Volume is jointly proportional to height and the square of the radius. For a constant volume, this means the radius is inversely proportional to the square root of the height.
The multiplier of height from the small cylinder to the larger one is 5/17. This means the multiplier of the radius will be √(17/5) ≈ 1.8439.
The radius of the larger cylinder will be ((9 cm)/2)×1.8439 ≈ 8.3 cm.
