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# 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 valu

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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

### Best Answer

#2
+91773
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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
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### 4+0 Answers

#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
+91773
+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
#3
+82576
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Very nice, Melody......

CPhill  Jun 12, 2015
#4
+91773
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Thanks Chris :)

Melody  Jun 13, 2015

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