Question

$<b><i><h1>▶QUESTION▶ </b></i></h1>$



A solid cylinder has total surface area of 462 cm² is curved area is one third of its total surface area. Find the volume of cylinder [ take π = 22/7 ]

Answer 1

$\huge{\boxed{\red {\bf{Answer}}}}$

$\huge\underline{\purple{\textbf{Given}}}$

$<b>$
TSA of cylinder = 462 cm²
CSA of cylinder = 462 × 1/3 = 154 cm²

So, 2πrh = 154 cm²

$\underline{ \textbf {\textit{By the given condition}}}$

$\rm 462 = 154 + 2\pi rh^2 \\ \implies \rm \cancel{308} \: = \: \cancel{2}\pi r^2 \\ \implies \rm 154 \: = \: \pi r ^2 \\ \implies \: \rm r^2 \: = \: \frac{ \cancel{154} \: \times \: 7 }{ \cancel{22}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 49 \\ \\ \implies \rm r \: = \: 7 \\ \\ \\ \rm \bf{2\pi rh \: = \: 154 }\\ \implies \rm h \: = \: \frac{154 \: \times \: 7}{2 \: \times \: 22 \: 7} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \rm\frac{7}{2}$

h = 7/2 = 3.5 cm

∴ r = 7 cm

∴ Volume = πr²h
= 22/7 × 7 × 7 × 3.5

= 539 cm³

$\huge\underline{\green {\bf{539 \: cm^3}}}$

$<font color = purple>$

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