A solid cone is melted and recast into smaller cones of the same height but half the radius. How many smaller cones can be made?
Show answer & explanation
Correct answer: B
Explanation
Volume of a cone = (1/3)πr²h
Let the radius of the large cone be r and the height be h.
Then, the volume of the large cone = (1/3)πr²h
Radius of the small cone = r/2
Height = h (same)
Therefore, the volume of the small cone = (1/3)π(r/2)²h
= (1/3)π(r²/4)h
= 1/4 × (1/3)πr²h
This means the volume of a small cone is 1/4 of the volume of the large cone.
Therefore, the number of small cones that can be formed = 1 ÷ (1/4)= 4