Question

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

Answer 1

Given, inner diameter $\left(d\right)=54cm$

Inner radius, $r=\frac{54}{2}=27cm$

Thickness $\left(t\right)=9cm$

Outer radius,$R=r+t=27+9=36cm$

Height of cylindrical roller,$h=1m=100cm$

We know that-

Step 1 : To find the volume of cylindrical roller

Volume of cylindrical roller

$$\begin{gathered} =\pi (R^2-r^2)h \\ =\frac{22}{7}\times ({36}^2-{27}^2)\times 100 \\ =\frac{22}{7}\times 567\times 100 \\ =178200c{m}^3 \end{gathered}$$

Step 2 : To find the weight of the roller

We have given that $1c{m}^3$iron weighs$8gm$

So, Weight of the roller

$$\begin{gathered} =Volume\times density \\ =178200\times 8gm \\ =1425600gm \\ =1425.6kg \end{gathered}$$

Hence, the weight of the roller is$1425.6kg$.