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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: 15
A right circular cylinder with radius 6 units and height 10 units is [#permalink]

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07 Oct 2017, 22:09
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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 ?
[Reveal] Spoiler: OA

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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, 01:37
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] 08 Oct 2017, 01:37
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