Question

A solid metallic cylinder of diameter 12 cm and height 15 cm is melted and recast into toys each in the shape of a cone of radius 3 cm and height 9 cm. Find the number of toys so formed.

Answer 1

$\frak{Given}\begin{cases}\sf{\:\:\; Diameter_{\:(cylinder)} = 12\:cm}\\\sf{\;\;\;Height_{\:(cylinder)} = 15\;cm}\\\sf{\:\:\; Radius_{\;(cone)} = 3\; cm}\\\sf{\:\;\; Height_{\:(cone)} = 9\;cm}\\\sf{\;\;\;Radius_{\: (cylinder)} = \dfrac{D}{2} = \cancel\dfrac{12}{2}=6\;cm}\end{cases}$

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$\underline{\bigstar\:\textsf{Let's Head to the Question Now :}}$

• Let the number of toys formed be x.

$:\implies\sf x \times Volume\;of\;conical\;toy = Volume\;of\; cylinder\\\\\\:\implies\sf x \Bigg(\dfrac{1}{3} \pi r^2 h \Bigg) = \pi r^2 h\\\\\\:\implies\sf x = \dfrac{\cancel{\pi}\; r^2 h}{1/3 \:\cancel{\pi}\; r^2 h}\\\\\\:\implies\sf x = \dfrac{3 r^2h}{r^2h}\\\\\\:\implies\sf x = \dfrac{\cancel{\;3}\;\times (6)^2 \times15}{3^2\times \cancel{\;9}}\\\\\\:\implies\sf x = \dfrac{6 \times 6 \times 15}{27}\\\\\\:\implies\sf x = \cancel\dfrac{540}{27}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 20}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence, \;the\; total\;number\;of\;toys\;formed\;are\;\bf{20 }.}}}$

Answer 2

Given :

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• Diameter of cylinder = 12cm
• Height of cylinder = 15cm
• Radius of cylinder = D/2 = 12/2 = 6cm
• Radius of cone = 3cm
• Height of cone = 9cm

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Need to find :

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• The number of toys formed.

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Solution :

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⧠ Let the number of toys formed be x.

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Therefore, x × vol. of conical toys = vol. of cylinder

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$\implies\bf{x×\cfrac{1}{3}πr^2h=πr^2h}$

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$\implies\bf{x×\cfrac{1}{3}π×3×3×9=π×6×6×15}$

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$\implies\bf{x=\cfrac{π×6×6×15×3}{\cfrac{π}{3}×3×3×9}}$

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$\implies\bf{x=20}$

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Hence, 20 toys are formed.