Question

The sum of the radius and height of a cylinder is 35 cm its total surface area is 1540 cm sq what is the volume of the cylinder

Answer 1

GivEn:

• The sum of the radius and height of a cylinder is 35 cm.

• Total surface of Cylinder is 1540 cm²

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To find:

• Volume of cylinder.

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SoluTion:

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As per givEn Question,

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$\bf Here \begin{cases} & \text{(r + h) = 35} \\ & \text{TSA of Cylinder = \sf 1540 cm^3 } \end{cases}$

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So , As we know that,

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$\star\;{\boxed{\sf{\purple{TSA\;of\;cylinder = 2 \pi r(r + h)}}}}$

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Therefore,

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$:\implies\sf 2 \times \dfrac{22}{7} \times r(35) = 1540$

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$:\implies\sf 2 \times \dfrac{22}{ \cancel{7}} \times r( \cancel{35}) = 1540$

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$:\implies\sf 2 \times 22 \times r \times 5 = 1540$

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$:\implies\sf 44 \times r \times 5 = 1540$

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$:\implies\sf r = \dfrac{1540}{44 \times 5}$

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$:\implies\sf r = \cancel{ \dfrac{1540}{220}}$

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$:\implies\bf \pink{r = 7\;cm}$

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GivEn that,

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$:\implies\sf r + h = 35$

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$:\implies\sf 7 + h = 35$

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$:\implies\sf h = 35 - 7$

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$:\implies\bf \pink{h = 28\;cm}$

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${\underline{\sf{\bigstar\;Now,\;we\;have\;to\;find\;volume\;of\;cylinder,}}}$

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As we know that,

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$\star\;{\boxed{\sf{\purple{Volume\;of\;cylinder = \dfrac{1}{3} \pi r^2h}}}}$

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$\;\;\;\;{\underline{\sf{Putting\;values\;:}}}$

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$:\implies\sf V = \dfrac{1}{3} \times \dfrac{22}{7} \times 7 \times 7 \times 28$

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$:\implies\sf V = \dfrac{1}{3} \times \dfrac{22}{ \cancel{7}} \times \cancel{7} \times 7 \times 28$

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$:\implies\sf V = \dfrac{1}{3} \times 22 \times 7 \times 28$

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$:\implies\sf V = \dfrac{1}{3} \times 4312$

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$:\implies\sf V = \dfrac{4312}{3}$

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$:\implies{\underline{\boxed{\sf{\purple{1437.33\;cm^3 \;(approx)}}}}}\;\bigstar$

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$\therefore$ Hence, The volume of cylinder is 1437.33 cm³