Question

The volume of a right circular cone of height 14cm is 168 cm3

. The radius of the cone is​

Answer 1

Given

• Volume of cone = 168 cm³
• Height of cone(h) = 14cm

To Find

• Radius of cone(r) = ?

Using Formula

$\tt Volume \: of \: right \: circular \: cone = \frac{\pi \: r {}^{2} h}{3}$

Solution

$\tt \implies Volume \: of \: cone = \frac{\pi \: r {}^{2}h }{3} \\ \tt \implies \: 168cm {}^{3} = \: \frac{\pi \times r {}^{2} \times 14}{3} cm {}^{3} \\ \tt \implies \: 168cm {}^{3} \times 3 = \: \frac{22}{7} \times 14 \times r {}^{2} \\ \tt \implies 504cm {}^{3} = \frac{308}{7} r {}^{2} \\ \tt \implies 504 \times 7 = 308r {}^{2} \\ \tt \implies \: 3528cm {}^{3} = \: 308r{}^{2} \\ \tt \implies r{}^{2} = \frac{3528}{308} \\ \tt \implies \: r{}^{2} = \: \frac{882}{77} \\ \tt \implies \: r = \: \sqrt{11.45} \\ \tt \implies r = 3.39cm$

Hence, radius of cone is 3.39cm.

Answer 2

Given ,

• The volume of right circular cone = 168 cm³
• Height of right circular cone = 14 cm

We know that , the volume of right circular cone is given by

$\sf \star \: \: \fbox{Volume = \frac{\pi {(r)}^{2}h }{2} }$

Thus ,

$\Rightarrow \sf 168 = \frac{22 \times {(r)}^{2} \times \cancel{14}}{ \cancel{7} \times 3} \\ \\\Rightarrow \sf 504 = 44 \times {(r)}^{2} \\ \\ \Rightarrow \sf {(r)}^{2} = \frac{504}{44} \\ \\ \Rightarrow \sf {(r)}^{2} = 11.45\\ \\\Rightarrow \sf r = \sqrt{11.45} \\ \\\Rightarrow \sf r = 3.39 \: \: cm$

$\therefore \sf \bold{ \underline{The \: radius \: is \: 3.39 \: cm}}$