Question

If $1c{m}^3$ of cast iron weighs $21g,$ find the weight of a cast-iron pipe of length $1m$ with a bore of $3cm$ in which the thickness of the metal is $1cm.$

Answer 1

External radius $=1.5+1=2.5cm,$
length $=100cm$
$\therefore$ External volume $=[\pi \times (2.25{)}^2\times 100$ ] $c{m}^3$
internal radius $=1.5cm$
$\therefore$ internal volume $=[\pi \times (1.5{)}^2\times 100$ ] $c{m}^3$
Volume of metal $=$ external volume $-$ internal volume
$=[\pi \times (2.5{)}^2\times 100-\pi \times (2.5{)}^2\times 100$ ] $c{m}^3$
$=\pi \times 100\times \left[\right(2.5{)}^2-\left(1.5{)}^2\right]$ $c{m}^3$

$=100\pi \times (2.5+1.5)(2.5-1.5)$ $[\because (a^2-b^2)=(a-b\left)\right(a+b\left)\right]$

$=100\pi \times 4\times 1$

Weight of cast iron $1c{m}^3=21g$

Total weight of cast iron $=$

$=(\frac{22}{7}\times 100\times 4\times 1\times \frac{21}{1000})$ kg
$=26.4kg.$