Question

A cylinder is open at both ends and is made of 1.5 cm thick metal. Its external diameter is 12 cm and height is 84 cm. What is the volume of metal used in making the cylinder? Also, find the weight of the cylinder if 1 cm 3 of the metal weighs 7.5 g.

Answer 1

Thickness of the metal =1.5 cm.

External diameter =12 cm.

$\therefore$ External radius (R)$=\frac{12}{2}=6cm.$

and then internal radius (r)=6-1.5

=4.5 cm.

Height (h)=84 cm.

$\therefore$ Volume of metal used $=\pi R^{2}h-\pi r^{2}h$

$=\pi h(R^2-r^2)$

$=\pi h(R+r)(R-r)$

$=\frac{22}{7}\times 84(6+4.5)(6-4.5)c{m}^2$

$=264\left(10.5\right)\left(1.5\right)c{m}^2=4158c{m}^3$

Weight of $1c{m}^3=7.5g$

$\therefore$ Total weight $=7.5\times 4158g$

=31185 g =31.185 kg.