A conical vessel of radius 6cm, height 8cm is completely filled with water A sphere is kept into the - Maths -

Question

A conical vessel of radius 6cm, height 8cm is completely filled
with water A sphere is kept into the water and its size is such
that when it touches the sides it is first immersed What fraction
of water overflows?
Give me the complete solution

Harleen Birdi · Accepted Answer

Dear Student! Here is the answer to your question

Radius (R) of conical vessel = 6 cm Height (H) of conical vessel = 8 cm volume of conical vessel (Vc) $= \frac{1}{3} π R^{2} H$ $= \frac{1}{3} \times π \times 6^{2} \times 8 = 96 π {cm}^{3}$ Let the radius of the sphere be r cm In right Î”PO'R, by Pythagoras theorem: l2 = 62 + 82 $\Rightarrow l = \sqrt{36 + 64} = 10 cm$ Hence, sin Î¸ $= \frac{O'P}{PR} = \frac{6}{10} = \frac{3}{5} (1)$ In right Î”MRO, $\sin θ = \frac{OM}{OR} = \frac{r}{OR}$ $\Rightarrow \frac{3}{5} = \frac{r}{8 - r} (Using (1) and O'R = O'O + OR \Rightarrow OR = O'R - O'O = 8 - r)$ â‡’ 24 â€“ 3r = 5r â‡’ 8r = 24 â‡’ r = 3 cm âˆ´ Volume of sphere (Vs) $= \frac{4}{3} π r^{3} = \frac{4}{3} π (3)^{3} {cm}^{3} = 36 π {cm}^{3}$ Now, Volume of the water = Volume of cone (Vc) = 96 Ï€ cm3 Clearly, Volume of the water that flows out of cone is same as the volume of the sphere i e Vs âˆ´ Fraction of the water that flows out $\frac{V_{s}}{V_{c}} = \frac{36 π}{96 π} = 3 : 8$ Cheers !!

A conical vessel of radius 6cm, height 8cm is completely filled with water. A sphere is kept into the water and its size is such that when it touches the sides it is first immersed. What fraction of water overflows? Give me the complete solution.

A conical vessel of radius 6cm, height 8cm is completely filled with water. A sphere is kept into the water and its size is such that when it touches the sides it is first immersed. What fraction of water overflows?

Give me the complete solution.