Question

The diameter of a cone is 28 cm and slant height is 10.5 cm. Then, its lateral surface area is :

(A) 480 cm2 (B) 490 cm2 (C) 462 cm2 (D) 466 cm2​

Answer 1

$\underline{\underline{\underline{\underline{\mathfrak{\blue{ \:\:\:Solution:-\:\:\:}}}}}}$

$\leadsto\bf \dfrac{Diameter}{2} = Radius$

$\leadsto\bf \cancel\dfrac{28}{2} = Radius$

$\leadsto\underline{\boxed{\textsf{ {\textbf{462 cm²}}}}} \qquad\qquad \bigg\lgroup\bold{Radius } \bigg\rgroup$

$\small\underline\textsf{ Formula Used:- }$

${\underline{\overline{\mid{\mathsf{\purple{\:\: Curved \:surface\: area\: of\: circle = \pi rl\:\:} \mid}}}}}$

$\small\underline\textsf{ Putting the values:-}$

$\leadsto\bf Curved\: surface \:area \:of \:circle = \dfrac{22}{7} \times \cancel{14} \times 10.5$

$\leadsto \bf Curved\: surface \:area\: of \:circle = 44 \times 10.5$

$\leadsto\bf Curved \:surface \:area \:of \:circle = 462 cm^2$

$\small\underline\textsf{ Hence:-}$

$\underline{\boxed{\textsf{Lateral surface area = {\textbf{462 cm²}}}}} \qquad\qquad \bigg\lgroup\bold{Option \ C \ is \ Correct } \bigg\rgroup$