Question

the volume of the cone is 6280cm³ and its base radius is 20cm. find it's perpendicular height (π = 3.14)​

Answer 1

Given : The volume of the cone is 6280cm³ and its base radius is 20 cm .

Need To Find : Perpendicular Height of Cone .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider the Perpendicular Height of Cone be x.

$\frak {\underline {\dag As, \: We \:know\:that \:: }}$

⠀⠀⠀⠀⠀$\underline {\boxed { \sf{ Volume _{(Cone)} = \dfrac{1}{3} \pi r^{2} h \:cu.units }}}$

⠀⠀⠀⠀⠀Here r is the Radius of Cone in cm , h is the Height of Cone & $\pi = \dfrac{21}{7} \:or \:3.14$ and we have given with the Volume of Cone is 6280 cm³ .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

⠀⠀⠀⠀⠀$:\implies \tt { 6280 cm^{3} = \dfrac{1}{3} \pi \times 20^{2} \times x \:}$

⠀⠀⠀⠀⠀$:\implies \tt { 6280 cm^{3} = \dfrac{1}{3} \times 3.14 \times 20 \times 20 \times x \:}$

⠀⠀⠀⠀⠀$:\implies \tt { 6280 cm^{3} = \dfrac{1}{3} \times 3.14 \times 400 \times x \:}$

⠀⠀⠀⠀⠀$:\implies \tt { \dfrac{6280 \times 3 }{3.14 \times 400 } = x \:}$

⠀⠀⠀⠀⠀$:\implies \tt { \dfrac{6280 \times 3 }{ 1,256 } = x \:}$

⠀⠀⠀⠀⠀$:\implies \tt { \dfrac{\cancel {18840}}{\cancel {1256} } = x \:}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 15\: cm}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Perpendicular\:Height \:of\:Cone \:is\:\bf{15\: cm}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀