A solid cone with a radius of 6 centimeters and a height of 8 centimeters is melted down to form small spheres, each with a radius of 2 centimeters. How many such spheres can be made?
Show answer & explanation
Correct answer: B
Explanation
Cone: r = 6 cm, h = 8 cm
Sphere: r = 2 cm
Volume of the cone = (1/3)πr²h
Volume of the sphere = (4/3)πr³
Volume of the cone = (1/3)π(6²)(8) = 96π
Volume of one sphere = (4/3)π(2³) = 32/3 π
Number of spheres = 96π ÷ (32/3 π) = 9