Question

37) A vessel is in the shape of an inverted cone. Its height is 8cm and radius is 5cm. It is filled
with full of water, if we drop some spheres of radius 0.5cm in this vessel, one forth of
the water expels. Find how many spheres are in the vessel.​

Answer 1

Answer:

Hope it helps you mate

Step-by-step explanation:

Volume of displaced water = volume of sphere .( by Archemedes Principle)

& In the following image PA = √(64+36)= 10 cm ( by Pythagoras law)

triangle PCA ~ triangle PBO ( by AA similarity corollary)

=> CA/BO = PA/PO ( csst)

=> 6/r = 10/ (8-r)

=> 10r = 48- 6r

=> 16r = 48

=> r = 3 cm

So, volume of sphere = 4/3 pi r^3

= 4/3 * pi * 27 = 36 pi cu cm

volume of displaced water = 36 pi cu cm

Now volume of cone = 1/3 pi * 36 * 8 = 96pi cu cm

So, fraction of water = Volume of displaced water / volume of cone

= 36 pi / 96 pi = 3/8 or 3:8 ………Ans