Question

A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm .The metal everywhere is 0.4 cm thick. The volume of the metal used is

• A. $316.24c{m}^3$
• B. $306.24c{m}^3$
• C. $356.24c{m}^3$
• D. $300.24c{m}^3$

Answer 1

The correct option is B $306.24c{m}^3$

Internal diameter = 11.2 cm
$\Rightarrow$ Internal radius (r) = $\frac{11.2}{2}=5.6cm$

External radius (R) = 5.6 + 0.4 = 6 cm
Length of the tube (h) = 21 cm

Volume of the metal used
= Volume of the cylinder with external radius (R) – Volume of the cylinder with internal radius (r)

$=\pi R^{2}h-\pi r^{2}h$

$=\pi h(R^2-r^2)=\left(\frac{22}{7}\right)\times 21\left[\right(6{)}^2-\left(5.6{)}^2\right]$

$=\left(\frac{22}{7}\right)\times 21\times (6+5.6)(6-5.6)$

$=\left(\frac{22}{7}\right)\times 21\times 11.6\times 0.4$

$=306.24c{m}^3$