Question

A conical vessel, with base radius 5 cm and height 24 cm is full of water this water is emptied into a cylindrical vessel of base radius 10cm find the height to which the water will rise in the cylindrical vessel

Answer 1

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Answer 2

Answer:

The water rises upto 2 cm of height of the cylindrical vessel.

Step-by-step explanation:

Given:

Radius of the Conical Vessel (r) = 5 cm

Height of the Conical Vessel (h) = 24 cm

Radius of the Cylindrical Vessel (R) = 10 cm

Let us assume the height of the Cylinder as H.

Formula used to find the Volume Of Cylinder:

$\pi r^{2} h$

Formula used to find the Volume of Cone:

$1/3 \pi r^{2} h$

Let us assume the height of the Cylindrical Vessel as x.

Volume of Water in the Conical Vessel = Volume of Water in the Cylindrical vessel

=> $\pi r^{2} h$ = $1/3 \pi R^{2} H$

=> $r^{2} h$ = $1/3 R^{2} H$

Substituting the values of Radius and Heights in the following equation:

=> 5 * 5 * 24 = 3 * 10 * 10 H

=> 25 * 24 = 300 * H

=> 600 = 300H

=> H = 600 / 300 = 2

Therefore, the water rises upto 2 cm of height of the cylindrical vessel.