#### Question

The `3/4` th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

#### Solution

Radius of conical vessel r = 5 cm

Height of conical vessel h = 24 cm

The volume of water = `3/4` ×volume of conical vessel

`= 3/4 xx 1/3 pir^2h`

`3/4 xx 1/3 pi xx 25 xx 24`

= 150

Let h' be the height of cylindrical vessel, which filled by the water of conical vessel,

Radius of cylindrical vessel = 10 cm

Clearly,

Volume of cylindrical vessel = volume of water

`pi(10)^2h = 150`

=> h = 1.5 cm

Thus, the height of cylindrical vessel is 1.5 cm.

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Solution The 3/4th Part of a Conical Vessel of Internal Radius 5 Cm and Height 24 Cm is Full of Water. the Water is Emptied into a Cylindrical Vessel with Internal Radius 10 Cm. Find the Height of Concept: Surface Areas and Volumes Examples and Solutions.