Question

$\sf\purple{Maths\:Legends\:please\:Help\:me...!!}$

The dimension of a solid iron cuboid arw 4.4 m x 2.6 m x 1.0 m . It is melted and react into a hollow cylindrical pipe of 30cm inner radius and thickness 5 cm. Find the length of the pipe.

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Answer 1

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Answer 2

Given : The dimension of a solid iron cuboid arw 4.4m x 2.6m x 1.0m & It is melted and react into a hollow cylindrical pipe of 30cm inner radius and thickness 5cm.

To Find : Find the length of the pipe ?

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Solution : Let the inner and outer radius of the cylinder pipe be r and R.

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Where,

• Inner radius r = 30cm
• Thickness = 5cm
• Outer radius R = 30 + 5 => 35cm

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Now,

• Length of the cuboid = 4.4m or 440cm
• Breadth of the cuboid = 2.6m or 260cm
• Height of the cuboid = 1m or 100cm

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Here,

• Volume of the cuboid = Volume of the cylinder pipe.

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$\pmb{\sf{\underline{According~ to~ the~ Given ~Question~:}}}$

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$\qquad{\sf:\implies{440~×~260~×~100~=~π\bigg(R^2~-~r^2\bigg)h}}$

$\qquad{\sf:\implies{440~×~260~×~100~=~\dfrac{22}{7}~×~\bigg(35^2~-~30^2\bigg)~×~h}}$

$\qquad{\sf:\implies{11440000~=~\dfrac{22}{7}~×~\bigg(1225~-~900\bigg)~×~h}}$

$\qquad{\sf:\implies{h~=~\dfrac{\bigg(11440000~×~7\bigg)}{\bigg(325~×~22\bigg)}}}$

$\qquad{\sf:\implies{\cancel\dfrac{80080000}{7150}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{11200~cm}}}}}}$★

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Therefore,

• ${\sf{\dfrac{112\cancel{00}~\cancel{c}m}{112\cancel{00}~\cancel{c}m}}}$

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Hence,

$\therefore\underline{\sf{The~ length ~of ~the ~pipe~ is~\bf{\underline{\pmb{112~m}}}}}$