P varies directly with Q means that as Q increases, P will also increase in proportion to Q. In this case, P varies with the cube of Q, so if Q increases by a factor of 2, P will increase by a factor of 2^3.
Therefore, if P = 4 when Q = 8, we can find the value of P when Q = 64 by using the formula:
P = kQ^3
where k is a constant
Substituting Q = 8 and P = 4 into the equation, we get:
4 = k(8^3)
Solved for k:
k = 1/64
So, the formula for P is:
P = (1/64) * Q^3
Thus, when Q = 64, we have:
P = (1/64) * 64^3
P = 16
So P = 16 when Q = 64.
