W varies directly as r cubed and inversely as s. If w=24 when r= 4 and s= 8, find out when w= 81 and s= 27

a) Given that w=81 and k = 0.375 then r = 6

b)  Given that s=27 and k = 224 then w=32

Step-by-step explanation:

Step(i):-

Given that W varies directly as r³

      ⇒ w∝r³

    ⇒   w = kr³

where 'k' is proportionally constant

given that w= 24 and r =4

     ⇒  24 = k (4)³

     ⇒ k =

    ⇒ k = 0.375

Step(ii):-

Given that W varies indirectly as 's'

            w ∝

            W =k

where 'k' is proportionally constant

          28 = k ()

        k = 28 × 8 = 224

Step(iii):-

a) Given that w=81 and k = 0.375

     w = kr³

   81 = 0.375 (r)³

   r³ = 216

  r = ∛216 =6

 r =6

b)

 Given that s=27 and k = 224

          W =k

         w = 224 ()

        w = 32