Question

A conical vessel has radius 10 cm and height 18cm and is completely filled with water which istransferred in a cylindrical vessel of radius 5
cm. Find the level of water (height) incylindrical vessel.


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Answer 1

For Conical vessel

Radius (r) = 10 cm

Height (h) = 18 cm

For Cylindrical vessel

Radius (r') = 5 cm

Height (h') = ?

Volume of water in cone = Volume of water in cylinder

Volume of cone = 1/3 πr^2 h

Volume of cylinder = πr'^2h'

1/3 πr^2h = πr'^2h

r^2h = 3r'^2h'

(10)^2(18) = 3(5)^2(h')

100 × 18 = 3 × 25 × h'

1800 = 75 × h'

h' = 75/1800

h' = 24 cm

Therefore, the level of water ( height ) in cylindrical vessel is 24 cm.

Answer 2

Answer :-

The level of water (height) incylindrical vessel is 24 cm.

Solution :-

Radius of the conical vessel (r) = 10 cm

Height of the conical vessel (h) = 18 cm

Volume of the conical vessel = 1/3 πr²h

= 1/3 * π * 10 * 10 * 18

= π * 6 * 100

Volume of the cylindrical vessel = 600π cm³

Radius of the cylindrical vessel (r) = 5 cm

Let the height of the cylindrical vessel be 'h' cm

Water in cylindrical vessel is transferred in a cylindrical vessel

So Volume of the cylindrical vessel = Volume of a conical vessel

⇒ πr²h = 600π cm³

⇒ π * 5 * 5 * h = 600π

⇒ π * 25 * h = 600π

⇒ h = 600π/(25π)

⇒ h = 600/25

⇒ h = 24 cm

Therefore the level of water (height) incylindrical vessel is 24 cm.