Question

The curved surface area of a right circular cylinder is half of its total surface area. Find the radius of the base of the cylinder if total surface area is 616cm2

Answer 1

$\textbf{Given:}$

$\textsf{The curved surface area of a right circular cylinder}$

$\textsf{is half of its total surface area and}$

$\textsf{total surface area is 616 square cm}$

$\textbf{To find:}$

$\textsf{Radius of the base of the cylinder}$

$\mathsf{}$

$\textbf{Solution:}$

$\textsf{Let r and h be radius and height of the given cylinder respectively}$

$\textbf{Formula used:}$

$\boxed{\begin{minipage}{8cm} \\\textsf{Curved surface area of cylinder}\mathsf{=2\,\pi\,r\,h\;square\;units}\\\\\textsf{Total surface area of cylinder}\mathsf{=2\,\pi\,r(h+r)\;square\;units}\\ \end{minipage}}$

$\mathsf{Consider,}$

$\mathsf{C.S.A=\dfrac{1}{2}{\times}T.S.A}$

$\mathsf{C.S.A=\dfrac{1}{2}{\times}616}$

$\mathsf{C.S.A=308\,cm^2}$

$\mathsf{2\,\pi\,r\,h=308}$

$\implies\boxed{\mathsf{2\pi\,r\,h=308}}$

$\mathsf{T.S.A=616\;cm^2}$

$\mathsf{2\,\pi\,r(h+r)=616}$

$\mathsf{2\,\pi\,r\,h+2\,\pi\,r^2=616}$

$\mathsf{308+2\,\pi\,r^2=616}$

$\mathsf{2\,\pi\,r^2=616-308}$

$\mathsf{2\,\pi\,r^2=308}$

$\mathsf{\pi\,r^2=154}$

$\mathsf{\dfrac{22}{7}{\times}r^2=154}$

$\mathsf{r^2=\dfrac{7{\times}154}{22}}$

$\mathsf{r^2=7{\times}7}$

$\mathsf{r^2=49}$

$\implies\boxed{\mathsf{r=7\;cm}}$

$\textbf{Answer:}$

$\textsf{Radius of base of the cylinder is 7 cm}$

$\textbf{Find more:}$

Volume of a cylinder is 2376cm cube. If the diameter of its base is 12 cm,then find its height

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The curved surface area of a cylinder is 1320 cm² and its base had diameter 21 cm. Find the height and the volume of the cylinder.[Use π = 22/7]

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