A cone is melted and recast into smaller cones with one-fourth the radius and one-fourth the height. How many such small cones can be formed?
Show answer & explanation
Correct answer: D
Explanation
Given:
Radius of the small cone = R/4
Height of the small cone = H/4
According to the formula:
Volume of a cone = (1/3)πr²h
Volume of the large cone = (1/3)πR²H
Volume of the small cone = (1/3)π(R/4)²(H/4)
= (1/3)π(R²/16)(H/4)
= (1/3)πR²H/64
Number of small cones = Volume of the large cone / Volume of the small cone
= ((1/3)πR²H) / ((1/3)πR²H/64)
= 64