Two solid right cones of equal height and of radii r1 and r2 are melted and made to form a solid sphere of radius R. Then the height of the cone is
A. $$\frac{{4{R^2}}}{{r_1^2r_2^2}}$$
B. $$\frac{{4R}}{{{r_1}{r_2}}}$$
C. $$\frac{{4{R^3}}}{{r_1^2 + r_2^2}}$$
D. $$\frac{{{R^2}}}{{r_1^2r_2^2}}$$
Answer: Option C
Solution (By Examveda Team)
$$\eqalign{ & {\text{Let the height be }}H \cr & \Rightarrow \frac{1}{3}\pi r_1^2H + \frac{1}{3}\pi r_2^2H = \frac{4}{3}\pi {R^3} \cr & \Rightarrow \frac{1}{3}\pi H\left( {r_1^2 + r_2^2} \right) = \frac{4}{3}\pi {R^3} \cr & \Rightarrow H = \frac{{4{R^3}}}{{r_1^2 + r_2^2}} \cr} $$This Question Belongs to Arithmetic Ability >> Mensuration 3D
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