Question

The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28cm. The length of the pipe is 35cm. Find the mass of the pipe, if 1cm³ of wood has mass of 0.6g​

Answer 1

Question:-

The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28cm. The length of the pipe is 35cm. Find the mass of the pipe, if 1cm³ of wood has mass of 0.6g

$\huge\mathcal\colorbox{white}{{\color{black}{☆Solution☆}}}$

Given:-

$\: \: \: \: \: \: \: \: \rm{Inner diametre = 24 cm}$

$\rm{\therefore \: Inner \: radius (r_1) = \frac{24}{2} = 12}$

$\rm{and \: Outer \: diameter(r_2) = 28cm }$

$\rm{\therefore Outer \: radius(r_2) = \frac{28}{2}= 14cm}$

$\rm{and \: height(h) = 35cm}$

$\small\boxed{{\fcolorbox{green}{white}{Volume of cylindrical wooden pipe~~—}}}$

$\rm{= Outer \: volume - Inner \: volume = π(r^2_2– r_1^2)h}$

$\sf{=\frac{22}{7}(14^2 – 12^2)×35}$

$= \sf{\frac{22}{7}(14+12)(14-12)×35}$

$\sf{=22×26×2×5 \: = \: 5720cm^3}$

$\bf{\because \: Mass \: of \: 1cm^3 \: of \: wood = 0.6g}$

$\rm{\therefore Mass \: of \: 5720cm^3 \: of \: wood = 0.6×5720}$

$\rm{= 3432g = (\frac{3432}{1000})kg}$

$\: \: \: \: \: \: \: \: \: \: \: \small\boxed{= 3.432 \: kg}$

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More to know :-

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Volume of a Hollow Cylinder —

↬ A hollow cylinder will be obtain by subtracting the interior volume from the exterior volume.

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i.e.

Volume = Exterior volume - Interior volume

⠀⠀⠀⠀⠀= πR²h - πr²h

「 Volume of a hollow cylinder 」

⠀⠀⠀⠀⠀⠀⠀⠀= π ( R² -r² ) h

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Where, R and r are exterior and interior radius respectively, h is the height of that hollow cylinder.

Answer 2

3.432kg

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