a hollow garden roller of 42cm diameter and length152cm is made of cast iron 2cm thick find the volume of iron used in the roller

Dear Student,

Please find below the solution to the asked query:

Given : Hollow garden roller of 42 cm diameter , So

Outer radius of roller ( Cylindrical in shape ) = R =  21 cm

And roller made of cast iron 2 cm thick , So

Inner radius of roller ( Cylindrical in shape ) = r =  21 - 2 =  19 cm

And length = 152 cm , So

Height of roller ( Cylindrical in shape ) = h =  152 cm

We know volume of hollow cylinder  = $\mathrm{\pi }$h ( R² - r² ) , So

We know : ( a² - b² ) = ( a - b ) ( a + b )

Volume of iron used in the roller = $\frac{22}{7}\times 152\times \left({21}^2 - {19}^2\right)= \frac{{\displaystyle 22}}{{\displaystyle 7}}\times 152\times \left(21 - 19\right)\left(21 +19 \right)= \frac{{\displaystyle 22}}{{\displaystyle 7}}\times 152\times 2 \times 40 = \frac{267520}{7} = \mathbf{38217}\mathbf{.}\mathbf{14}\mathbf{ }{\mathbf{cm}}^{\mathbf{3}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$

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