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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 - CBSE Class 10 - Mathematics

ConceptSurface Areas and Volumes Examples and Solutions

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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APPEARS IN

RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Ex. 14.10 | Q: 72 | Page no. 32

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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.
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