A hollow sphere of external and internal diameter 6 cm and 4 cm respectively is melted into a cone o...........

Quantitative Aptitude (CDS) Mensuration 3D

A hollow sphere of external and internal diameter 6 cm and 4 cm respectively is melted into a cone of base diameter 8 cm . What is the height of the cone?

4.75 cm

5.50 cm

6.25 cm

6.75 cm

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Explanation:

Volume of sphere = volume of cone
4/3 $\pi$ (R_ext³ - R_int³) = 1/3 $\pi$ R_c²Hc
H_c= 4(R_ext³ - R_int³) / R_c² = 4(3³ - 2³)/ R_c²given (R_c=D_c/2=8/2=4)
= 4(27-8)/16= 19/4= 4.75 cm