Question

The value of a silver coin varies directly as the square of its diameter, when thickness is constant and varies directly as its thickness when diameter remains constant. Two silver coins have the diameters in the ratio 4 : 3. Find the ratio of the thickness if the value of the first coin is four times the value of the second coin

Answer 1

Let value be denoted by V, diameter by D, thickness by T

V = D2T

V1 = 16T1

V2 = 9T2

Here, V1 = 4*V2 => 16*T1 = 36*T2

T1/T2 = 36/16 = 9:4

Answer 2

The ratio of the thickness of the coins is 9:4.

Diameter of the silver coins = 4:3 ( Given)

Let the value of silver coins be = V

Let the diameter of silver coins be = D

Let the thickness of silver coins be = T

Therefore,

V = D²T

V1 = 16T1

V2 = 9T2

Here, V1 = 4V = 16T1  = 36T2

T1/T2 = 36/16

= 9/4

Thus, the ratio of the thickness is 9:4.