Question

the total surface area of a cone whose radius is 3cm and slant height is 18 cm will be ______​

Answer 1

Given that , The Radius of a cone is 3 cm & The slant Height of cone is 18 cm .

Exigency To Find : Total Surface Area of cone ?

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⠀⠀⌬⠀We've the radius and slant height of cone . Formula to Find Total Surface Area of Vone is Given by —

$\qquad \qquad \star\:\: \underline{\boxed {\pmb{\frak {T.S.A \:_{\:(\:Cone\:)\:}\:=\:\pi \:r\:(\: r\:+\:l\:)\:\:sq.units\:}}}}$

⠀⠀⠀⠀Here , r is the Radius of Cone & l is the slant height of cone .

$\\\dag\:\underline {\frak{ \:Putting \:known \:Values \:in \:Formula \:-\::\:}}$

$\\\qquad \dashrightarrow \sf T.S.A \:_{\:(\:Cone\:)\:}\:=\:\pi \:r\:\big(\: r\:+\:l\:\big)\:\\\\\\ \qquad \dashrightarrow \sf T.S.A \:_{\:(\:Cone\:)\:}\:=\:\dfrac{22}{7} \times \:3 \:\big(\: 3\:+\:18\:\big)\:\\\\\\ \qquad \dashrightarrow \sf T.S.A \:_{\:(\:Cone\:)\:}\:=\:\dfrac{22}{7} \times \:3 \:\big(\: 21\:\big)\:\\\\\\ \qquad \dashrightarrow \sf T.S.A \:_{\:(\:Cone\:)\:}\:=\:\dfrac{22}{\cancel {7}} \times \:3 \:\times\: \cancel{21}\:\:\\\\\\ \qquad \dashrightarrow \sf T.S.A \:_{\:(\:Cone\:)\:}\:=\:22 \times \:3 \:\times\: 3\:\:\\\\\\\qquad \dashrightarrow \sf T.S.A \:_{\:(\:Cone\:)\:}\:=\:22 \times \:9\:\:\\\\\\ \qquad \dashrightarrow \underline {\boxed {\pmb{\frak{\purple { T.S.A \:_{\:(\:Cone\:)\:}\:=\:198\: cm^2\:}}}}}\:\:\bigstar \:$

$\therefore \:\underline {\sf Hence, \:The \:Total \:Surface \:of \:Cone \:is \:\pmb{\bf 198 \:cm^2\:}.\:}$