The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times as fast as radius. When the radius is 1 cm the altitude is 6 cm. When the radius is 6 cm then volume is increasing at the rate of 1 cm³/sec. When the radius is 36 cm the volume is increasing at a rate of n cm³/sec. The value of n is equal to:
a. 12
b. 22
c. 30
d. 33