Question

A sphere, a cylinder and a cone are of the same radius and same height. Find the ratio of their curved

surface areas​

Answer 1

${ \large{ \sf{ \underbrace{\underline{\bigstar \: Answer}}}}}$

${ \small{ \boxed{ \red{ \underline{ \bf \:Since}}}}}$

$\small\color{magenta}{the \:height \:of \:a sphere \:is \:the \:diameter,\: the\: cone \:and \:cylinder\: have\: height \:2r.}$

$\textbf\color{blue}{Then Curved surface area of Sphere}$

$\huge\color{purple}{= 4πr²}$

$\textbf\color{green}{Curved surface area of cylinder }$

$\huge\color{purple}{= 2πr(2r) = 4πr²}$

$\textbf\color{brown}{Curved surface area of cone}$

$\huge\color{gold}{= πrl}$

$\tt\color{pink}{where,}$

$\small\color{darkgreen}{l = √(r2 + h2 ) = √( r2 + (2r)2) = √(5r2) = r√5}$

$\textbf\color{brown}{Curved surface area of cone}$

$\huge\color{lime}{= π√5r2}$

$\bold{Now,}$

Ratio of CSA 's a sphere ,cylinder and a cone

$\mapsto\bf{4πr2:2πrh : πrl}$

$\mapsto\bf{4πr2:4πr2 : πr2√5}$

$\color{green}\boxed{\sf{= 4 : 4 : √5}}$

Thankyou :)

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