A lamb grows rapidly, with its mass proportional to the cube of its length. When the lambs length changes by 15.8%, its mass increases by 17.3kg. Find the lambs mass at the end of the process.

Question

A lamb grows rapidly, with its mass proportional to the cube of its length. When the lambs length changes by  15.8%, its mass increases by 17.3kg. Find the lambs mass at the end of the process.

lalaly · Answer

initial length=L
mass=m
m = kL^3
increase in length is 15.8%
final length = L + 15.8L/100 = 1.158L
final mass = m + 17.3

m + 17.3 = k x (1.158L)^3
m + 17.3 = 1.55kL^3
m + 17.3 = 1.55m
0.55m = 17.3
m = 31.45

final mass = 31.45 + 17.30 = 48.75 kg