Question

The inner radius of a cylinder of a cylinder and the base radius of a solid cone are equal when this cone is fully immersed in the completely filled cylinder,1/4 of volume of liquid falls out what is the ratio of yhe heights of cylinder and cone

Answer 1

Ratio of the heights of cylinder and cone = 4:3

Given:

i) The inner radius of a cylinder and the base radius of a solid cone are equal

ii) When this cone is fully immersed in the completely filled cylinder, 1/4 of volume of liquid falls out

To find:

Ratio of the heights of cylinder and cone

Solution:

Let the inner radius of a cylinder be denoted as r.

Since, the inner radius of cylinder and the base radius of solid cone are equal, the base radius of solid cone = r

Let the height of cylinder = h1 and the height of  solid cone = h2

Hence,

Volume of cylinder = $\pi$r²(h1)

Volume of solid cone = (1/3)$\pi$r²(h2)

Applying the archimedes principle,

Volume of solid cone = Volume of liquid which falls out

=> Volume of solid cone = (1/4) Volume of cylinder

=> (1/3)$\pi$r²(h2) = (1/4) ($\pi$r²(h1))

=> (1/3)(h2) = (1/4)(h1)

=> h1/h2 = 4/3

Hence,

the ratio of the heights of cylinder and cone = 4:3

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