Question

X varies inversely as the cube of Y. If X = 1 when Y = 2 , then find the constant of variation.

• A. 1
• B. 2
• C. 4
• D. 8

Answer 1

The correct option is D 8

Given, X varies inversely as the cube of Y.
$\Rightarrow X\propto \frac{1}{Y^3}$
Let the constant of variation be k.
$\Rightarrow X=\frac{k}{Y^3}$
$\Rightarrow X{Y}^3=k$
Given, at X = 1, Y = 2.
So, $k=X{Y}^3=\left(1\right)\left(2^3\right)=8$.