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Cone

by vidhya16 » Sat Jan 21, 2012 12:17 pm
A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

(1) The top surface of the water in the cone is currently square centimeters in area.
(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically.
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by pemdas » Sat Jan 21, 2012 2:06 pm
out of so many words only simple cone derived data :(
(pi*r^2*h)/3 is volume of cone, given h=4r and (pi*r^2*4r)/3
we need to answer one question to solve this - how much water is in the cone now (also we must consider the value of r)
st(1) implies there is another cone inside this big cone (water itself in the cone shape) and it's square is 1 (cm.^2). Sufficient, as we know about the similar properties of two cones (they share the same lateral sides and height). Basically, the original cone's apex is calculated by considering h=4r (!)
st(2) supplies the length fragment on the height between two bases of cones, but this Not Sufficient, as the difference per se can be 4 and 1004-1000 or 10-6 with different squares in bases and various volumes

a
vidhya16 wrote:A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

(1) The top surface of the water in the cone is currently square centimeters in area.
(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically.
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by [email protected] » Sun Jan 22, 2012 5:41 pm
Could any of the experts please help me explain this question...
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by Anurag@Gurome » Sun Jan 22, 2012 5:59 pm
vidhya16 wrote:A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

(1) The top surface of the water in the cone is currently square centimeters in area.
(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically.
Image

(1) I feel some info is missing from statement 1, it should be some number, say x cm² = (pi)r².
Since x is given so we can find r from the above equation.
Given that H = 2 * 2R or R/H = 1/4
R/H = r/h = 1/4 implies r/h = 1/4, we know r, so we can find h from here.
Hence we can find the values of volume, V = (1/3) * (pi)r²h; SUFFICIENT.

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically implies h + 4 = H, which is one equation and 2 variables, so we don't know the exact values; NOT sufficient.

The correct answer is A.
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by harrybm » Wed Jan 25, 2012 1:47 am
Anurag@Gurome wrote:
vidhya16 wrote:A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

(1) The top surface of the water in the cone is currently square centimeters in area.
(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically.
Image

(1) I feel some info is missing from statement 1, it should be some number, say x cm² = (pi)r².
Since x is given so we can find r from the above equation.
Given that H = 2 * 2R or R/H = 1/4
R/H = r/h = 1/4 implies r/h = 1/4, we know r, so we can find h from here.
Hence we can find the values of volume, V = (1/3) * (pi)r²h; SUFFICIENT.

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically implies h + 4 = H, which is one equation and 2 variables, so we don't know the exact values; NOT sufficient.

The correct answer is A.

Thanks anurag, but Im still a little bit lost. I understand Option A will give us the measurement of the big cone, however to be able to measure the volume of small cone filled with water, dont we need information B. and that smaller volume then divided by the rate 2 cubic meter per hour. Can you kindly help me on this? Thanks
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by [email protected] » Mon May 07, 2012 3:11 am
Anuraaag!!! as such the Cone is out of portion for the GMAT, but you never know with what is being asked...
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

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