A conical vessel of radius 6cm and height 8cm is completely filled with water a sphere
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Radius (R) of conical vessel = 6 cm
Height (H) of conical vessel = 8 cm
volume of conical vessel (Vc)
= 1/3πr^2h
= 1/3π × 36 × 8
= 96π
Let the radius of the sphere be r cm.
In right ΔPO'R, by Pythagoras theorem:
L = √(64 + 36)
L = 10 cm
Hence sin@ = O'P / PR = 6/10 = 3/5
In right triangle MRO
Sin@ = OM /OR = r / OR
3/5 = r / (8 - r)
⇒ 24 – 3r = 5r
⇒ 8r = 24
⇒ r = 3 cm
∴ Volume of sphere (Vs)
Now,
Volume of the water = Volume of cone (Vc) = 96 π cm3
Clearly, Volume of the water that flows out of cone is same as the volume of the sphere i.e. Vs.
∴ Fraction of the water that flows out
Vs/Vc = 36π / 96π = 3/8
Vs : Vc = 3 : 8
Hope it helps...
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I dont know sorry i will try to do it
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