Question

. Two solids of right cylindrical shape are 49 cm and
35 cm high and their base diameters are 16 cm and
14 cm respectively. Both are melted and moulded
into a single cylinder. If the height of new cylinder is
99 cm, find the diameter of the base of the cylinder.​

Answer 1

Answer:

Hope it helps you..............

Answer 2

GivEn:

• Diameter of 1st cylinder, $\sf d_1$ = 16 cm
• Radius of 1st cylinder, $\sf r_1$ = 8 cm
• Diameter of 2nd cylinder, $\sf d_2$ = 14 cm
• Radius of cylinder, $\sf r_2$ = 7 cm
• Height of 1st cylinder, $\sf h_1$ = 49 cm
• Height of 2nd cylinder, $\sf h_2$ = 35 cm
• Height of new cylinder, h = 99 cm

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To find:

• Base diameter of new cylinder

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SoluTion:

$\dag\;{\underline{\frak{We\;know\;that,}}}$

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$\star\;{\boxed{\sf{\purple{Volume_{\;(cylinder)} = \pi r^2 h_1}}}}$

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Therefore,

${\underline{\sf{\bigstar\;Volume\;of\;1st\;cylinder\;:}}}$

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$:\implies\sf \pi (r_1)^2 h$

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$\dag\;{\underline{\frak{Putting\;values,}}}$

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$:\implies\sf \dfrac{22}{7} \times 8 \times 8 \times 49$

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$:\implies\sf \dfrac{22}{ \cancel{7}} \times 8 \times 8 \times \cancel{49}$

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$:\implies\sf 22 \times 8 \times 8 \times 7$

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$:\implies{\underline{\boxed{\sf{\pink{9856\;cm^3}}}}}\;\bigstar$

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${\underline{\sf{\bigstar\;Volume\;of\;2nd\;cylinder\;:}}}$

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$:\implies\sf \pi (r_2)^2 h_2$

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$\dag\;{\underline{\frak{Putting\;values,}}}$

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$:\implies\sf \dfrac{22}{7} \times 7 \times 7 \times 35$

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$:\implies\sf \dfrac{22}{ \cancel{7}} \times 7 \times 7 \times \cancel{35}$

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$:\implies\sf 22 \times 7 \times 7 \times 5$

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$:\implies{\underline{\boxed{\sf{\pink{5390\;cm^3}}}}}\;\bigstar$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \: the \: Question :}}}}\mid}$

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☯ Both cylinders are melted and moulded into a single cylinder.

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Therefore,

$\star\;\sf Volume\;of\;new\;cylinder = Volume\;of\;1st\;cylinder + Volume\;of\;2nd\;cylinder$

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$:\implies\sf 9856 + 5390$

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$:\implies{\underline{\boxed{\sf{\purple{15246\;cm^3}}}}}\;\bigstar$

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☯ Let radius of new cylinder be r cm.

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$\dag\;{\underline{\frak{Putting\;values,}}}$

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$:\implies\sf 15246 = \dfrac{22}{7} \times r^2 \times 99$

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$:\implies\sf 15246 = \dfrac{2178}{7} \times r^2$

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$:\implies\sf r^2 = \dfrac{15246 \times 7}{2178}$

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$:\implies\sf r^2 = \dfrac{106722}{2178}$

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$:\implies\sf r^2 = \cancel{ \dfrac{106722}{2178}}$

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$:\implies\sf r^2 = 49$

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$:\implies\sf \sqrt{r^2} = \sqrt{49}$

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$:\implies{\underline{\boxed{\sf{\red{r = 7\;cm}}}}}\;\bigstar$

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Therefore,

★ Diameter of new cylinder = 2 × 7 = 14 cm

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$\therefore$ Hence, Diameter of new cylinder is 14 cm.