Two spheres of radius 6 cm and 4cm are inscribed in a right circular cone.The bigger sphere touches the smaller one and also the base of cone .find the height of the cone?

Answer 1

Draw a cross-section diagram of the situation.
the sides of the cone would be tangent to both circles.
draw radii of both circles to a side of the cone, with the right angle as they meet the side
Let the remaining distance from the top of the smaller circle to the vertex of the cone be x cm
I see two similar right-angled triangles, so we can use ratios

(x+4)/4 = (x+14)/6
6x + 24 = 4x + 56
2x = 32
x = 16

So the height = 12 + 8 + x = 36 cm