Question

The radius and slant height of a cone are in the ratio of 4 : 7. If its curved surface area is 792 cm², find its radius. (Use π=22/7)

Answer 1

Answer:

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Answer 2

AnsweR :

Radius = 12 cm.

$\bf{\Large{\underline{\sf{Given\::}}}}$

The radius and slant height of a cone are in the ratio of 4:7. If its curved surface area is 792 cm².

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

It's radius.

$\bf{\Large{\underline{\rm{\purple{Explanation\::}}}}}$

Let the ratio be R.

$\bf{\red{We\:have}\begin{cases}\sf{Radius\:of\:cone\:(r)=4R}\\ \sf{Slant\:height\:of\:cone\:(h)=7R}\\ \sf{Curved\:surface\:area\:of\:cone\:=\:792cm^{2} }\end{cases}}$

A/q

Formula Use :

$\bf{\large{\boxed{\sf{C.S.A.\:of\:cone\:=\:\pi rl\:\:\:\:(sq.unit)}}}}}$

$|\implies\tt{\pi rl\:=\:792cm^{2} }\\\\\\\\|\implies\tt{\dfrac{22}{\cancel{7}} *4R*\cancel{7}R\:=\:792}\\\\\\\\|\implies\tt{22*4R^{2} \:=\:792}\\\\\\\\|\implies\tt{88R^{2} \:=\:792}\\\\\\\\|\implies\tt{R^{2} \:=\:\cancel{\dfrac{792}{88} }}\\\\\\\\|\implies\tt{R^{2} \:=\:9}\\\\\\\\|\implies\tt{R\:=\:\sqrt{9} }\\\\\\\\|\implies\tt{\purple{R\:=\:3\:cm}}$

Thus,

The radius of cone = 4(3) cm  = 12 cm.