Question

A cylindrical tube open at both ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm then find how many cubic centimeters of iron has been used in making the tube?

Answer 1

Step 1: Finding the outer radius(R) and inner radius(r)

We have outer diameter = 16 cm.

Therefore, outer radius, $R=\frac{16}{2}=8cm$

Since the thickness is 2 cm, therefore, the inner radius would be:

$r=8-2=6cm$

Step 2: Finding the volume of iron(V) used

We know that the volume of a hollow cylinder with outer radius R, inner radius ‘r’ and heigh ‘h’ is given as:

$V=\mathrm{\pi h}\left({\mathrm{R}}^2-{\mathrm{r}}^2\right)$

Substituting the values we get,

$$\begin{gathered} V=\frac{22}{7}\times 100\times \left(8^2-6^2\right)\left(Here,h=100cm,\mathrm{\pi }=\frac{22}{7}\right) \\ =\frac{22}{7}\times 100\times \left(64-36\right) \\ =\frac{22}{7}\times 100\times \left(28\right) \\ =22\times 100\times 4 \\ =8800c{m}^3 \end{gathered}$$

Final answer: Therefore, 8800 cm³ of iron has been used in making the tube