Find the radius of the circular base of the cone, if its volume is $154c{{m}^{3}}$ and the perpendicular height is 12 cm. - Noon Academy

Find the radius of the circular base of the cone, if its volume is $154c{{m}^{3}}$ and the perpendicular height is 12 cm.

Class 10 | Frank | ICSE | Maths | Mensuration II

Find the radius of the circular base of the cone, if its volume is $154c{{m}^{3}}$ and the perpendicular height is 12 cm.

According to the given question,

The volume of circular based cone is $154c{{m}^{3}}$ .

The perpendicular height of the circular based cone is 12 cm.

We know that, volume of the cone is $\frac{1}{3}\times \left( \pi {{r}^{2}} \right)\times h$

So, we have to find the radius of the cone,

$\frac{1}{3}\times \left( \pi {{r}^{2}} \right)\times h=154$

$\frac{1}{3}\times \left( \left( \frac{22}{7} \right)\times {{r}^{2}} \right)\times 12=154$

${{r}^{2}}=\frac{\left( 154\times 3\times 7 \right)}{\left( 12\times 22 \right)}$

${{r}^{2}}=12.25$

$r=\sqrt{12.25}$

$r=3.5cm$ Therefore, the radius of the circular base of the cone is 3.5 cm.

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