Question

If a cylinder of radius 2cm and height 15cm is melted and the same mass is used to create a sphere.Then the radius of the sphere is​

Answer 1

Answer:

the answer is radius of sphere is 20.12cm.

Answer 2

GivEn:

• Radius of Cylinder (r) = 2 cm

• Height of Cylinder = 15 cm

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To find:

• Radius of sphere

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SoluTion:

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Let radius of sphere be R cm.

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${\underline{\sf{\bigstar\;As\;per\:given\;quesTion\;:}}}$

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A cylinder is melted to create a sphere of the same mass.

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$:\implies\sf \red{Volume_{\;(cylinder)} = Volume_{\;(sphere)}}$

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$:\implies\sf \pi r^2 h = \dfrac{4}{3} \pi R^3$

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$:\implies\sf \cancel{\pi} r^2 h = \dfrac{4}{3} \cancel{\pi} R^3$

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$:\implies\sf r^2h = \dfrac{4}{3}R^3$

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

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$:\implies\sf (2)^2 \times 15 = \dfrac{4}{3} \times R^3$

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$:\implies\sf \cancel{4} \times 15 \times \dfrac{3}{ \cancel{4}} = R^3$

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$:\implies\sf 15 \times 3 = R^3$

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$:\implies\sf 45 = R^3$

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$\small\;\;\;\;\sf \underline{Taking\;cube\;root\;both\;sides\;:}$

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$:\implies\sf \sqrt[3]{45} = \sqrt[3]{R^3}$

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$:\implies\sf{\underline{\boxed{\bf{\purple{20.12\;cm\;(approx)}}}}}\;\bigstar$

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$\therefore$ Hence, Radius of Sphere is 20.12 cm.