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CBSE Class 10 Answered

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and it's size is such that when it touches the sides it is just immersed. What fraction of the water overflows ?
Asked by adityaagrawal020503 | 09 Feb, 2019, 09:21: AM
answered-by-expert Expert Answer
 
Figure shows a sphere is just immersed in water contained in a conical vessel.
Volume of overflowing water equals volume of sphere. To get the radius of sphere, we need to find the biggest circle
that can be enclosed inside the cone ABC.

Let O be the centre of circle and we draw perpendicular OD and OE. Let the radius OD be r cm
 
CD is tangent to the circle and CD = 3cm and begin mathsize 12px style angle end styleOCD = (1/2)begin mathsize 12px style angle end styleECD = (1/2)tan-1(8/3) ≈35°
we have OD = r = CD×tanbegin mathsize 12px style angle end styleOCD = 3 × tan(35) ≈ 2 cm.
hence fraction of overflowing water = begin mathsize 12px style fraction numerator begin display style 4 over 3 straight pi cross times 2 cubed end style over denominator begin display style 1 third cross times straight pi cross times 3 squared cross times 8 end style end fraction space equals space 4 over 9 end style
Answered by Thiyagarajan K | 10 Feb, 2019, 01:13: PM

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