Question

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

Answer 1

Step1:Finding volume of cylinder

According to the given details

Outer diameter $D=16cm$

Height $=length=100cm$

Thickness of iron sheet $=2cm$

Outer radius$R=\frac{16}{2}=8cm$

Volume of cylinder

$$\begin{gathered} =\pi R^{2}h \\ =\frac{22}{7}\times 8^2\times 100 \\ =\frac{140800}{7}c{m}^3 \end{gathered}$$

Step2: finding volume of hollow space

Now, inner diameter $d$

$$\begin{gathered} =outerdiameter–2\times thicknessofironsheet \\ =16-2\times 2 \\ =16-4 \\ =12cm \end{gathered}$$

Inner radius $r=\frac{12}{2}=6cm$

Thus, Volume of hollow space

$$\begin{gathered} =\pi r^{2}h \\ =\frac{22}{7}\times 6^2\times 100 \\ =\frac{79200}{7}c{m}^3 \end{gathered}$$

Step3: Finding volume of iron used

Volume of iron used

$$\begin{gathered} =Volumeofcylinder–Volumeofhollowspace \\ =\frac{140800}{7}-\frac{79200}{7} \\ =\frac{61600}{7} \\ =8,800c{m}^3 \end{gathered}$$

Answer

Hence, the volume of iron used is $8,800c{m}^3$.