Help needed ASAP (1 Viewer)

[Topher15]

i have this question due tomorrow and im stuck:
A cone having the the height 12cm and radius 5cm fits into a sphere, find the radius of the shere.
i am seriously stumped any help would be greatly appreciated.

 

[PC]

The slant height of the cone is 13 cm. (Use Pythagoras' Theorem.)

Now it's similar triangles. Draw a diagram of the cone, and try to fit it inside a cylinder. Draw a right angled triangle. The shortest side is 5 cm (radius of cone), the middle side is 12 cm (height of cone) and the longest side is 13 cm (slant height).

Now extend the "height" of the cone to the base of the sphere. Join the base of the sphere to the side of the other triangle. Another right angled triangle.

You already know one side of this triangle (5 cm), so let the extended but from the height be x cm.

Now it's easy.
5/12 = x/5
12x = 25
x= 25/12

Diameter = 12 + 25/12 = 14 1/12 cm

Radius = 7 1/24 cm

Fun question!