Question

the radius of the cone is half of its height then it's volume is​

Answer 1

Given :

Radius of cone is half of its height

To find :

Volume of cone

Formula used :

Volume of cone = (1/3) π r² h

Solution :

Let, height of cone = h

therefore radius = (1/2) × Height

radius = h/2

Putting value of height and radius in formula of volume of cone

$\sf \implies \: Volume \: = \dfrac{1}{3} \pi { \dfrac{h}{2} }^{2} \times h \: \\ \\ \sf \implies \: Volume \: = \dfrac{1}{3} \times \dfrac{ {h}^{2} }{ {4} } \times h \\ \\ \sf \implies \: Volume \: = \dfrac{1}{12} {h}^{3} \\ \\ \sf \implies \: Volume \: = \bold {\dfrac{ {h}^{3} }{12} }$

ANSWER :

Volume = (Height)³ ÷ 12