Question

Please answer 21
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Tomorrow exam cbse

Answer 1

ok bro first of all best of luck for exam here is your answere

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