Question

the radius of the base and the height of a cylinder in the ratio is 2:3 .if it's volume is 1617 cm cube. find the total surface area of the cylinder. ​

Answer 1

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➡️R:H =2:3

➡️R/H = 2/3

➡️3r = 2h

$h = \frac{3r}{2}$

$\mathcal \orange{Now \: \pi {r}^{2} h = 1617cm}$

$\frac{22}{7} \times {r}^{2} \times \frac{3r}{2} \times 1617 \: cm$

${r}^{3} = \frac{1617 \times 7 \times 2}{22 \times 3}$

${r}^{3} = 343$

$r = \sqrt[3]{343}$

$r = 7cm$

$\red{\boxed{Now \: the \: height \: is \: 10.5cm}}$

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➡️TOTAL SURFACE AREA OF CYLINDER=>

$2\pi r{ </u><u>(</u><u>\: h + r</u><u>)</u><u>}$

$2 \times \frac{22 \times 7 }{7} \times 7 + 10.5$

$= 44 \times 17.5 \: sq \: cm$

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