Question

1) Given a cone 10 feet tall with a diameter of 10 feet, determine the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base.

Answer 1

the radius would be 3

Explanation:

so what it's saying si there;s a cone with diameter 10 and height 10, the 4 feet above the bottom of the cone is the base of the smaller cone. The height of the smaller cone becomes 6, making the diameter 6 as the ratio becomes 6:6, and radius is diameter/2 becoming 3

Answer 2

The radius of the base of the small cone is 3 feet

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;

`(Height \, of \, small \, cone)/(Height \, of \, larger\, cone) =(Diameter \, of \, base \, of \, small \, cone)/(Diameter \, of \, base \, of \, larger \ cone) =(6)/(10) = (x)/(10)`

Where:

x = The diameter of the base of the small cone

Therefore;

`{x} = (6)/(10) * 10 = 6 \, feet`

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.