Question

If the volume of a right circular come of hight 9 cm is 48πcm^3,find the diameter of this base.

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Answer 1

Step-by-step explanation:

Height of a cone = 9 cm Volume of cone = 48 π cm3 We know, Volume of cone = 1 3 πr2h 48π = 1 3 π r2 x 9 r2 = 16 or r = 4 Radius of base r = 4 cm Therefore, Diameter = 2 Radius = 2 x 4 cm = 8 cm.

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Answer 2

Given :

• Height of Cone is 9 cm .
• Volume of Cone is 48π cm³ .

To Find :

• Diameter of the base of Cone .

Solution :

$\longmapsto\tt{Height=9\:cm}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{48{\not{\pi}}=\dfrac{1}{3}{\not{\pi}}\times{{{r}^{2}}\times{9}}}$

$\longmapsto\tt{48\times{3}=9\times{{r}^{2}}}$

$\longmapsto\tt{144=9\:{r}^{2}}$

$\longmapsto\tt{\cancel\dfrac{144}{9}={r}^{2}}$

$\longmapsto\tt{16={r}^{2}}$

$\longmapsto\tt{\sqrt{16}=r}$

$\longmapsto\tt\bf{r=4\:cm}$

Now ,

As we know that Diameter is double of Radius . So ,

$\longmapsto\tt{Diameter=2r}$

$\longmapsto\tt{2(4)}$

$\longmapsto\tt\bf{8\:cm}$

So , The Diameter of the base of Cone is 8 cm .