The respective ratio of the curved surface ar | vedclass

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(B) Let the radius of the cylinder be $r$ and the height be $h$.The curved surface area $(CSA)$ is $2 \pi r h$ and the total surface area $(TSA)$ is $

Vedclass · Accepted Answer

$28$

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(B) Let the radius of the cylinder be $r$ and the height be $h$.The curved surface area $(CSA)$ is $2 \pi r h$ and the total surface area $(TSA)$ is $2 \pi r h + 2 \pi r^2$.The ratio is given as $CSA : TSA = 4 : 5$.$\frac{2 \pi r h}{2 \pi r h + 2 \pi r^2} = \frac{4}{5}$$\frac{h}{h + r} = \frac{4}{5}$$5h = 4h + 4r \implies h = 4r$.Given $CSA = 1232 \, cm^2$,we have $2 \pi r h = 1232$.Substitute $h = 4r$ into the equation:$2 	imes \frac{22}{7} 	imes r 	imes (4r) = 1232$$8 	imes \frac{22}{7} 	imes r^2 = 1232$$r^2 = 1232 	imes \frac{7}{8 	imes 22}$$r^2 = 1232 	imes \frac{7}{176} = 7 	imes 7 = 49$$r = 7 \, cm$.Since $h = 4r$,then $h = 4 	imes 7 = 28 \, cm$.

The respective ratio of the curved surface area and total surface area of a cylinder is $4:5$. If the curved surface area of the cylinder is $1232 \, cm^2$,what is the height? (in $cm$)

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