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16 Sep 2014, 00:35
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An open-topped right circular cylinder with a volume of 72 cubic meters is completely filled with water. Water evaporates from the cylinder at a constant rate of 2 liters per hour for every square meter of the top surface area. How long will it take for 30 liters of water to evaporate?
(1) The height of the cylinder is 2 meters.
(2) The radius of the base of the cylinder is \(\frac{6}{\sqrt{\pi} }\) meters.
(1) The height of the cylinder is 2 meters.
(2) The radius of the base of the cylinder is \(\frac{6}{\sqrt{\pi} }\) meters.
16 Sep 2014, 00:35
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Official Solution:
An open-topped right circular cylinder with a volume of 72 cubic meters is completely filled with water. Water evaporates from the cylinder at a constant rate of 2 liters per hour for every square meter of the top surface area. How long will it take for 30 liters of water to evaporate?
To determine the time required for 30 liters of water to evaporate, we need to find the surface area of the top of the cylinder: the evaporation rate is \(2 * area\) liters per hour, so the time needed is \(time = \frac{30}{2 *area}\).
Since the volume of the cylinder is given by \( volume= \pi{r^2}h = 72\), the top surface area is \(\text{area} = \pi{r^2} = \frac{72}{h}\). Therefore, we need either the top surface area or the height of the cylinder to find the time required for evaporation.
(1) The height of the cylinder is 2 meters.
As discussed, this information is sufficient.
(2) The radius of the base of the cylinder is \(\frac{6}{ \sqrt{\pi} }\) meters.
From this statement, we can calculate that the top surface area is \(area = \pi{r^2} = 36\). This information is also sufficient.
Answer: D
An open-topped right circular cylinder with a volume of 72 cubic meters is completely filled with water. Water evaporates from the cylinder at a constant rate of 2 liters per hour for every square meter of the top surface area. How long will it take for 30 liters of water to evaporate?
To determine the time required for 30 liters of water to evaporate, we need to find the surface area of the top of the cylinder: the evaporation rate is \(2 * area\) liters per hour, so the time needed is \(time = \frac{30}{2 *area}\).
Since the volume of the cylinder is given by \( volume= \pi{r^2}h = 72\), the top surface area is \(\text{area} = \pi{r^2} = \frac{72}{h}\). Therefore, we need either the top surface area or the height of the cylinder to find the time required for evaporation.
(1) The height of the cylinder is 2 meters.
As discussed, this information is sufficient.
(2) The radius of the base of the cylinder is \(\frac{6}{ \sqrt{\pi} }\) meters.
From this statement, we can calculate that the top surface area is \(area = \pi{r^2} = 36\). This information is also sufficient.
Answer: D
General Discussion
08 May 2023, 07:51
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
