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# A right circular cylinder with radius 6 units and height 10 units is

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Intern
Joined: 30 Aug 2017
Posts: 14
A right circular cylinder with radius 6 units and height 10 units is  [#permalink]

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07 Oct 2017, 23:09
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Difficulty:

55% (hard)

Question Stats:

61% (02:36) correct 39% (03:02) wrong based on 54 sessions

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A right circular cylinder with radius 6 units and height 10 units is placed upright and is filled up to 2/5th of its volume with water. a solid cone of radius 3 units and height 4 units is then submerged completely in the cylinder. what is the increase in the height of water level ?

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Intern
Joined: 28 Dec 2010
Posts: 49
Re: A right circular cylinder with radius 6 units and height 10 units is  [#permalink]

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08 Oct 2017, 02:37
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In this question, you just need to calculate the volume of solid cone. There is no need to calculate volume of cylinder to find the actual increase.

Volume of cone = $$\frac{1}{3}* π * r^2 * H$$

= $$\frac{1}{3}* π * 3^2 * 4$$

= $$12 π$$

Now how much volume would it displace in a cylinder, let the height be x.
Volume displaced = $$π * r^2 * H$$

$$12 π = π * 6^2 * x$$

$$1 = 3 * x$$

$$x = 1/3$$

A.
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Re: A right circular cylinder with radius 6 units and height 10 units is  [#permalink]

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05 Jan 2019, 07:04
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Fair enough. But could someone please explain that why we don’t really need to calculate the volume of the cylinder?

Moreover, I still don’t understand the logic behind the given solution

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Intern
Joined: 09 Jul 2018
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Re: A right circular cylinder with radius 6 units and height 10 units is  [#permalink]

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07 Jan 2019, 18:35
The maximum volume that the cone can displace is it's total volume
Hence we don't need to calculate the volume of the cyclinder!

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Re: A right circular cylinder with radius 6 units and height 10 units is  [#permalink]

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25 May 2019, 19:47
Fair enough. But could someone please explain that why we don’t really need to calculate the volume of the cylinder?

Moreover, I still don’t understand the logic behind the given solution

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By Archimedes' principle weight of the fluid displaced equals the weight of the submerged object.

Volume of cone= Volume of water risen.
Now find h from the formula of cylinder.
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Re: A right circular cylinder with radius 6 units and height 10 units is   [#permalink] 25 May 2019, 19:47
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