Question

A conical vessel of radius 8cm and height 15cm is completely filled with water.A sphere is lowered into the water such that when it touches the sides,it is just immersed as shown in the figure.What fraction of water overflows

Answer 1

Answer:

288/625

0.4608

Step-by-step explanation:

Let say radius of Sphere = r

Volume of Cone = Volume of Water = (1/3)π(8)² * 15 = 320π cm³

Slant height = √8² + 15²  = √289 = 17 cm

Sinθ = 8/17   (in Δ  POR)

Sinθ = OM/OR   ( (in Δ  MOR)

OM = radius of sphere = r

OR = 15 - r

=> r/(15 - r)  = 8/17

=> 17r = 120 - 8r

=> 25r = 120

=> r = 4.8 cm

Volume of sphere = (4/3)π r³  =  (4/3)π (4.8)³

= 147.456 π cm³

Volume of Water over flow = 147.456 π cm³

fraction of water overflows = 147.456 π / 320π

= 0.4608

= 4608/10000

= 288/625

Answer 2

Answer: 0.4608

Step-by-step explanation:

For proper answer see the image