Question

If the volume and the base area of a cone are 48pie cm3 and 12pie cm2 then the height of the cone is equal to

Answer 1

Given :

• Volume of Cone is 48π cm³ .
• Area of Base is 12π cm² .

To Find :

• Height of Cone .

Solution :

Firstly we will find Radius :

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Circle=\pi{{r}^{2}}}$

Putting Values :

$\longmapsto\tt{12{\not{\pi}}={\not{\pi}}\times{{r}^{2}}}$

$\longmapsto\tt\bf{12={r}^{2}}$

Now ,

For Height :

Using Formula :

$\longmapsto\tt\boxed{Volume\:of\:Cone=\dfrac{1}{3}\pi{{r}^{2}h}}$

Putting Values :

$\longmapsto\tt{48{\not{\pi}}=\dfrac{1}{3}\times{{\not{\pi}}}\times{12}\times{h}}$

$\longmapsto\tt{48=\dfrac{1}{3}\times{12}\times{h}}$

$\longmapsto\tt{h=\dfrac{{\cancel{48}}\times{3}}{{\cancel{12}}}}$

$\longmapsto\tt{h=4\times{3}}$

$\longmapsto\tt\bf{h=12\:cm}$

So , The Height of Cone is 12 cm ...