Two spheres of radii 6 cm and 1 cm are inscribed inside a right circular cone. T

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Two spheres of radii 6 cm and 1 cm are inscribed inside a right circular cone. The bigger sphere touches the smaller sphere and also the base of the cone. What is the height of the cone?

Options:

A . 14 cm

B . 12 cm

C .

\frac{85}{6}

cm

D .

\frac{72}{5}

cm

Answer: Option D
:
D

Soln: the triangles shown are similar. Hence $\frac{x + (1 + 6)}{x} = \frac{1}{6}$ ;x= $\frac{7}{5}$ ; Height of cone:13 + $(\frac{7}{5}) = \frac{72}{5}$ .

Hence, Ans: d)

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