Question

A solid iron rectangular block of dimensions $(2.2m\times 1.2m\times 1m)$ is cast into a hollow cylindrical pipe of internal radius $35cm$ and thickness $5cm$. Find the length of the pipe.

Answer 1

Solid iron block
Volume$=(2.2\times 1.2\times 1)$
$=2.64m^3$
Cylindrical pipe radius $\left(r_1\right)$$35㎝=0.35m$
thickness$=5cm$
$r_2=35+5=40㎝=0.4m$
Volume$=\pi (r_2^2-r_1^2)h$
$=\pi ({0.4}^2-{0.35}^2)h$
$=\pi (0.16-0.1225)h$
$=\pi \left(0.0375\right)h$
$\pi \left(0.0375\right)h$
$h=\frac{2.64}{0.0375}\times \frac{1}{\pi }$
$=\frac{2.64}{375}\times \frac{100}{22}\times 7$
$=\frac{16\times 7}{5}m$
$=\frac{112}{5}$
$=22.47m$
$=2247cm$