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

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;

$\frac{Height \, of \, small \, cone}{Height \, of \, larger\, cone} =\frac{Diameter \, of \, base \, of \, small \, cone}{Diameter \, of \, base \, of \, larger \ cone} =\frac{6}{10} = \frac{x}{10}$

Where:

x = The diameter of the base of the small cone

Therefore;

${x} = \frac{6}{10} \times 10 = 6 \, feet$

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.