EOV wrote:Hi everybody,
A certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water.
If between 12 and 16 cubic centimeters or the cube's volume is above the surface of the water, then the lengh of a side of the cube is approximately
A) 4
B) 5
C) 7
D) 8
E) 9
Would you help me to found correct answer.
Since 80% to 85% of the volume is BELOW the surface, 15% to 20% of the volume is ABOVE the surface.
Thus, when the volume above the surface increases by 4 cubic centimeters (from 12 to 16), the PERCENTAGE of the volume above the surface increases by 5% (from 15% to 20%).
The implication is that 4 cubic centimeters = 5% of the total volume:
4 = .05v
v = 4/.05 = 400/5 = 80.
Since v = e³, we get:
80 = e³
e = 80^(1/3) = 8^(1/3) * 10^(1/3) ≈ 2*2 ≈ 4.
The correct answer is
A.
An easier approach might be to plug in the answers.
I would start with A or B, since 4 and 5 are easy values to cube.
Answer choice B: 5
If e=5, then v = 5³ = 125.
Range above the surface:
15% of 125 = 18.75.
20% of 125 = 25.
Since the range above the surface must be between 12 and 16, the volume here is too great, implying that the edge must be LESS than 5 centimeters.
The correct answer is
A.
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