In an aerospace materials lab, a technician cuts a model of a right circular cone (height 12 cm, base radius 6 cm) horizontally at half its height to form a smaller, similar cone at the tip. What is the volume of the smaller cone formed?
Show answer & explanation
Correct answer: B
Explanation
Given:
Height of the original cone = 12 cm
Radius of the original cone = 6 cm
Height of the smaller cone = 6 cm
Formula:
Volume of the cone = (1/3)πr²h
Radius of the smaller cone = 6 × (6/12) = 3 cm
Volume of the smaller cone = (1/3)π × 3² × 6 = 18π
Volume of the smaller cone = 18π cm³