Rate and Ratio?

" value of a coin $V varies jointly as its thickness t mm and the square of its diameter d mm "
That is ,
v = k * t * d^2 , for some k
where v = value , t = thickness , d = diameter

t(A) : t(B) = 2 : 3
d(A) : d(B) = 3 : 2

v(A) : v(B)
= [ t(A) * d(A)^2 ] : [ t(B) * d(B)^2 ]
= ( 2 * 3^2 ) : ( 3 * 2^2 )
= 18 : 12
= 3 : 2

v(A) : v(B) = 3 : 2
v(B) = ( 2 / 3 ) * v(A) = ( 2 / 3 ) * 6000 = 4000

Ans: $4000