Question

T varies inversely with the cube of W. When W is 3, T is 1/9. Find the value of W when T is 1/243

Answer 1

T varies inversely with the cube of W 

$T = k/W^3$

$\frac{1}{9} = k/3^3$

$k = \dfrac{3^3}{9} = 3$

$W^3 = k/T$

$W = \sqrt[3]{ k/T }$

When $T=1/243$

$W = \sqrt[3]{ 3/(1/243)}= \sqrt[3]{729} = 9$