Suppose the rate of melting, M grams per second, of a sphere of ice is inversely proportional to the square of the radius, r cm. When r=20,M=0.6. Find the constant of proportionality.
The statement " y varies inversely as x means that when x increases, y decreases by the same factor. In other words, the expression xy is constant:
xy=k
where k is the constant of variation.
Here, it is given that the rate of melting M=0.6 g/sec of a sphere of ice is inversely proportional to the square of radius r=20 cm, therefore,
Mr2=k⇒0.6×(20)2=k⇒k=0.6×400⇒k=0.6×400⇒k=240
Hence, the constant of proportionality is 240.