If a ∝ b, b ∝ c let us show that a³b³ + b³c³ + c³a³∝ abc (a³ + b³ + c³).

Volume of a sphere varies directly with the cube of its radius. Three solid spheres having length of and metre diameter are melted and a new solid sphere is formed. Let us find the length of diameter of the new sphere. [let us consider that the volume of sphere remains same before and after melting]

y is a sum of two variables, one of which varies directly with x and another varies inversely with x. With x = - 1, then y = 1 and when x = 3, then y = 5. Let us find the relation between x and y.

To dig a well of x dcm deep. One part of the total expenses varies directly with x and other part varies directly with x². If the expenses of digging wells of 100 dcm and 200 dcm depths are ₹ 5000 and ₹ 12000 respectively, let us write by calculating the expenses of digging a well of 250 dcm depth.

Volume of a cylinder is in joint variation with square of the length of radius of base and its height, Ratio of radii of bases of two cylinders is 2 : 3 and ratio of their heights is 5 : 4, let us find the ratio of their volumes.