# A cylindrical road roller made of iron is 1 m wide . its inner diameter is 54 cm and thickness of the iron sheet rolled into the road roller is 9cm . Find the weight of the roller if 1 c.c. of iron weights 8gm .

Solution: The width of the road roller is $1m$  i.e  , 100$cm$

So,            Height (length) of the cylinder $=100cm$

Inner radius of the cylinder    $=r=\frac{54}{2}cm=27cm$

Thickness of the iron sheet$= 9cm$

$\therefore$              Outer radius of the cylinder $=R=(27+9)cm=36cm$

Thus ,       Volume of the iron sheet used $=(\pi R^2h-\pi r^2h)cm^3$

$=[\pi(R-r)(R+r)h]cm^3$

$=[3.14\times (36+27)(36-27)\times100]cm^3$

$=\frac{314}{100}\times63\times 9\times100=178038cm^3$

$\therefore$              Weight of the roller    $=178038\times8gms=178038\times \frac{8}{1000}Kgs=1424.304Kgs$

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