Question

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?

• A. 14 cm
• B. 12 cm
• C. 85/6 cm
• D. 72/5 cm

Answer 1

The correct option is D 72/5 cm

The triangles shown are similar.
$Hence\frac{x+(1+6)}{x}=\frac{6}{1}$
$x=\frac{7}{5}$
$Heightofcone:13+\left(\frac{7}{5}\right)$ = $\frac{72}{5}$