Question

Find the height of cone if its slant height 34cm and base diameter is 32 cm

Answer 1

Given : The slant height of cone is 34cm and base diameter is 32 cm .

Exigency To Find : Height of a cone .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Finding Base Radius of Cone .

• Radius of Cone = $\dfrac{Diameter}{2}$

Where,

• Diameter of Cone is 32 cm .

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

$\qquad:\implies \sf{Radius _{(Cone)} = \cancel {\dfrac{32}{2}}}\\\\:\implies\bf{Radius_{(Cone)} = 16cm}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Radius \:of\:Cone \:is\:\bf{16 \: cm}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀Finding Height of Cone :

As, We know that ,

$\star\:\:\boxed {\sf { Height = \sqrt { Slant \;Height ^2 - Radius ^2}}}$

Where,

• Slant Height = 34 cm
• Radius = 16 cm .

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

$:\implies \sf{ Height = \sqrt { 34^2 - 16^2 }}\\\\ :\implies \sf{ Height = \sqrt { 1156 - 256 }}\\\\ :\implies \sf{ Height = \sqrt { 900 }}\\\\ :\implies \bf{ Height = 90\:cm}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Height \:of\:Cone \:is\:\bf{30\: cm}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀