# Thread: Express h interms of x

1. ## Express h interms of x

The radius of the base of a cone is x cm and its height is h cm
The radius of a sphere is 2x cm
The v olume of the cone and the vilume of the sphere are equal
Express h in terms of x

So

$\displaystyle \frac{1}{3}\pi r^{2}h=\frac{4}{3}\pi r^{3}\rightarrow $$\displaystyle \text{cancel out pi and 1/3} \rightarrow x^2h=4*4x^2\rightarrow x^2h=16x^3\rightarrow h=16x^3-x^2=x^2(16x-1) note: I replaced the r with the x and 2x from circle and cone. Am I correct? 2. Originally Posted by Mukilab The radius of the base of a cone is x cm and its height is h cm The radius of a sphere is 2x cm The v olume of the cone and the vilume of the sphere are equal Express h in terms of x So \displaystyle \frac{1}{3}\pi r^{2}h=\frac{4}{3}\pi r^{3}\rightarrow$$\displaystyle \text{cancel out pi and 1/3} \rightarrow x^2h=4*4x^2\rightarrow x^2h=16x^3\rightarrow h=16x^3-x^2=x^2(16x-1)$ note: I replaced the r with the x and 2x from circle and cone. Am I correct?
$\displaystyle \frac{\pi}{3} x^2 h = \frac{4\pi}{3} (2x)^3$

$\displaystyle x^2 h = 4 (2x)^3$

$\displaystyle x^2 h = 32 x^3$

$\displaystyle h = 32x$

3. thanks, I should be more careful with my powers :P