Question

the volume of a cylinder is 6538 cubic metres and its height is 28 cm. find its radius and the curved surface area.
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Answer 1

$\bigstar\huge\bf\underline{\underline{Given:-}}$

$\longmapsto\sf Volume \ of \ a \ cylinder \ = \ 6538cm$

$\longmapsto\sf Its \ height \ = \ 28cm$

$\bigstar\huge\bf\underline{\underline{To \ find:-}}$

$\longmapsto\sf The \ radius \ and \ the \ curved \ surface \ area$

$\bigstar\huge\bf\underline{\underline{Solution:-}}$

$\sf According \ to \ problem$

$\sf Volume \ of \ cylinder \ = \ 6358cm$

$(\sf Volume \ of \ cylinder \ = \ \pi r^{2}h)$

$\hookrightarrow\sf \pi r^{2}h \ = \ 6358$

$\hookrightarrow\sf \pi r^{2}h \ = \ 6358$

$\hookrightarrow\sf r^{2}\times28 \ = \ 6358\times(22\div7)$

$\hookrightarrow\sf r^{2} \ = \ 72 . 25$

$\hookrightarrow\sf r \ = \sqrt{72.25}$

$\hookrightarrow\boxed{\sf radius \ = \ 8.5}$

$\sf Then,$

$\sf Curved \ surface \ area \ = \ 2\pi r^{2}h$

$\implies\sf 2\times(22\div7)\times8.5\times28$

$\implies\boxed{\boxed{\bf 1496}}$

Answer 2

$\huge \tt Given :$

• The volume of a cylinder is 6538 cubic metres
• Its height is 28 cm.

$\huge \tt To\: Find :$

• its radius
• curved surface area.

$\huge \tt Solution :$

$\sf Volume \ of \ cylinder \ = \ 6358cm$

$\sf Volume \ of \ cylinder \ = \ \pi r^{2}h$

$:\implies \sf \pi r^{2}h \ = \ 6358$

$:\implies \sf r^{2}\times28 \ = \ 6358\times(22\div7)$

$:\implies \sf r^{2} \ = \ 72 . 25$

$:\implies\sf r \ = \sqrt{72.25}$

$\boxed{\sf {\pink {radius \ = \ 8.5}}}$

$\sf Curved \ surface \ area \ = \ 2\pi r^{2}$

$:\implies\sf 2\times(22\div7)\times8.5\times2$

$\boxed{\sf {\pink {curved \: surface \: area \:= \: 1496}}}$

Explore more :

• $\sf surface \ area \ = \ 2\pi r^{2} + 2\pi rh$
• $\sf base \ area \ = \pi r^{2}$
• $\sf perimeter \ = 2\pi r$

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Hope it helps uh ! ☑