the curved surface area of a cone is A cm^2 the volume of at the cone is V cm^3 The height of the cone is h cm Given that V=3A find the value of h

* year nine maths hwk can you do it ?

Guest Jun 11, 2015

#2**+10 **

Anon is right BUT you can get h in term of r

$$\\A=\pi r\sqrt{h^2+r^2}\qquad V=\frac{\pi r^2h}{3}\qquad and \qquad V=3A\\

so \\

3\pi r\sqrt{h^2+r^2}=\frac{\pi r^2h}{3}\\\\

9\sqrt{h^2+r^2}= rh\\\\

81*(h^2+r^2)= r^2h^2\\\\

81h^2+81r^2= r^2h^2\\\\

81h^2-r^2h^2= -81r^2\\\\

h^2(81-r^2)= -81r^2\\\\

h^2= \frac{-81r^2}{81-r^2}\\\\

h^2= \frac{81r^2}{r^2-81}\\\\

h= \frac{9r}{\sqrt{r^2-81}}\;\;cm\\\\$$

Melody
Jun 12, 2015

#1**+5 **

no,Because there is equation between height and the radius of the cone,like 81*h^2+81*r^2=(hr)^2,h will change when r is change ,and exact value of r is not given

Guest Jun 11, 2015

#2**+10 **

Best Answer

Anon is right BUT you can get h in term of r

$$\\A=\pi r\sqrt{h^2+r^2}\qquad V=\frac{\pi r^2h}{3}\qquad and \qquad V=3A\\

so \\

3\pi r\sqrt{h^2+r^2}=\frac{\pi r^2h}{3}\\\\

9\sqrt{h^2+r^2}= rh\\\\

81*(h^2+r^2)= r^2h^2\\\\

81h^2+81r^2= r^2h^2\\\\

81h^2-r^2h^2= -81r^2\\\\

h^2(81-r^2)= -81r^2\\\\

h^2= \frac{-81r^2}{81-r^2}\\\\

h^2= \frac{81r^2}{r^2-81}\\\\

h= \frac{9r}{\sqrt{r^2-81}}\;\;cm\\\\$$

Melody
Jun 12, 2015