Question

the ratio of the curved surface area and the total surface area of a right circular cylinder is 5 ratio 7 find the ratio between the height and the radius

Answer 1

it should be 7 : 5 by given fig u can understand eas2

Answer 2

Given: The ratio between the CSA and the TSA of a right circular cylinder is 5:7.

To find: Ratio of height to the radius of the cylinder?

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☯ Let radius and height of a right circular cylinder be 'r' and 'h' respectively.

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

Ratio between the Curved surface area and the Total surface area of a right circular cylinder is 5:7.

5:7.⠀⠀⠀

$:\implies\sf \dfrac{CSA_{\;(cylinder)}}{TSA_{\;(cylinder)}} = \dfrac{5}{7}$

$:\implies\sf \dfrac{ \cancel{2 \pi r} h}{ \cancel{2 \pi r} (r + h)} = \dfrac{5}{7}$

$:\implies\sf \dfrac{h}{r + h} = \dfrac{5}{7}$

$:\implies\sf 7h = 5(r + h)$

$:\implies\sf 7h = 5r + 5h$

$:\implies\sf 7h - 5h = 5r$

$:\implies\sf 2h = 5r$

$:\implies\sf{\boxed{\sf{\pink{ \dfrac{h}{r} = \dfrac{5}{2} }}}}\;\bigstar$

$\therefore$ The ratio between height and radius of right circular cylinder is 5:2.

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