Answer:
The radius of the base of the small cone is 3 feet
Step-by-step explanation:
The question requires the determination of the radius of the smaller cone
Therefore, height of the larger cone = 10 feet
Base diameter of the larger cone = 10 feet
Height of horizontal plane of small plane above base of larger cone = 4 feet
Hence the height of the small cone = 6 feet
Therefore, by similar triangles, and tangents we have;
![\frac{Height \, of \, small \, cone}{Height \, of \, larger\, cone} =\frac{Diameter \, of \, base \, of \, small \, cone}{Diameter \, of \, base \, of \, larger \ cone} =\frac{6}{10} = \frac{x}{10}](https://tex.z-dn.net/?f=%5Cfrac%7BHeight%20%5C%2C%20of%20%5C%2C%20small%20%5C%2C%20cone%7D%7BHeight%20%5C%2C%20of%20%5C%2C%20larger%5C%2C%20cone%7D%20%3D%5Cfrac%7BDiameter%20%5C%2C%20of%20%5C%2C%20base%20%5C%2C%20of%20%5C%2C%20small%20%5C%2C%20cone%7D%7BDiameter%20%5C%2C%20of%20%5C%2C%20base%20%5C%2C%20of%20%5C%2C%20larger%20%5C%20cone%7D%20%3D%5Cfrac%7B6%7D%7B10%7D%20%3D%20%5Cfrac%7Bx%7D%7B10%7D)
Where:
x = The diameter of the base of the small cone
Therefore;
![{x} = \frac{6}{10} \times 10 = 6 \, feet](https://tex.z-dn.net/?f=%7Bx%7D%20%3D%20%5Cfrac%7B6%7D%7B10%7D%20%5Ctimes%2010%20%3D%206%20%5C%2C%20feet)
The radius of the base of the small cone = half the diameter of the base of the small cone
∴ The radius of the base of the small cone = (6 feet)/2 = 3 feet.