How many ball bearings can you make from a cone?

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Question from Vatsal, a student:

there is a sum in my maths book which states the following:
how many ball bearings of diameter 2.5 cm. can you get by melting a solid metallic cone of radius 20cm and a height of 5 meters?
how do i do this please tell me even the minute things like cancellations and where to
use = , ; or any such thing because I'm a bit weak in maths

Vatsal,

You need to find the volume of the cone and the volume of one of the ball bearings. Then you need to ask yourself "How many ball bearings can I make with the volume of molten metal I have from melting the cone?" Two of the measurements are in centimeters and one is in meters. You need them all in the same units so I'm going to use centimeters. Thus the cone is 500 cm high.

The volume of a cone is given by

V = 1/3 π r² h cubic centimeters

where r is the radius and h is the height, both in centimeters. Calculate the volume of the cone.

The volume of a sphere is given by

V = π r³ cubic centimeters

where r is the radius in centimeters. Calculate the volume of a ball bearing.

How many ball bearings can you make with the volume of metal obtained by melting the cone?

Harley

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