A solid cylinder of radius 3 cm and height 5 cm is melted to form tiny right circular cones, each with base radius 1 mm and height 1 cm. How many such cones can be made?
Aptitude
Volume and Surface Area
Difficulty: Medium
Choose an option
-
A3500
-
B13500
-
C4500
-
D7500
Answer
Correct Answer: 13500
Explanation
Introduction / Context:Melting and recasting conserves volume. We compute the cylinder volume and divide by the volume of one small cone to find the count of cones produced.
Given Data / Assumptions:
- Cylinder: r = 3 cm, h = 5 cm → V_cyl = πr^2h.
- Cone: base radius = 1 mm = 0.1 cm, height = 1 cm → V_cone = (1/3)πr^2h.
Concept / Approach:Number of cones n = V_cyl / V_cone (volumes in the same units). Convert millimetres to centimetres before substitution.
Step-by-Step Solution:
V_cyl = π * 3^2 * 5 = 45π cm^3V_cone = (1/3)π * (0.1)^2 * 1 = (1/3)π * 0.01 = π/300 cm^3n = 45π / (π/300) = 45 * 300 = 13500Verification / Alternative check:π cancels; ensure radius in cm (0.1 cm) to avoid 100× error.
Why Other Options Are Wrong:They arise from unit mistakes (using 1 mm as 1 cm) or misplacing the 1/3 in cone volume.
Common Pitfalls:Unit conversion errors; forgetting the 1/3 factor for cone volume; arithmetic slips during division.
Final Answer:13500