Question

A 14cm long electric pipe has external and internal radii respectively as $5cm$ and $3cm$ . Find the volume of the electric pipe.

Answer 1

Hint: At first, we find the volume of the solid pipe of radius $5cm$ according to the formula $V=\pi {{r}^{2}}h=\pi {{\left( 5 \right)}^{2}}\times 14=\pi \times 25\times 14=1099.557c{{m}^{3}}$ . Then, we find the volume of the solid pipe of radius $3cm$ according to the formula $V=\pi {{r}^{2}}h=\pi {{\left( 3 \right)}^{2}}\times 14=\pi \times 9\times 14=395.84c{{m}^{3}}$ . Then, we take the difference of these values which gives us the answer.

Complete step by step answer:
Let there be a cylinder of radius r and height h. The area of the base of the cylinder will be $A=\pi {{r}^{2}}$ and the volume of the cylinder will be the area times the height of the cylinder, that is, $V=\pi {{r}^{2}}\times h=\pi {{r}^{2}}h$ .
Now, if we observe carefully, an electric pipe is also a cylinder, except that it is hollow. We are given that the outer radius of the pipe is $5cm$ and the inner radius is $3cm$ . Now, we assume the pipe to be solid and of radius $5cm$ . The volume of the pipe will then be,
$\Rightarrow V=\pi {{\left( 5 \right)}^{2}}\times 14=\pi \times 25\times 14=1099.557c{{m}^{3}}$
But this volume is that for a solid pipe of radius $5cm$ . Again, we assume the pipe to be solid and of radius $3cm$ . The volume of the pipe will then be,
$\Rightarrow V=\pi {{\left( 3 \right)}^{2}}\times 14=\pi \times 9\times 14=395.84c{{m}^{3}}$
But this volume is that for a solid pipe of radius $3cm$ . Now, if we observe carefully, we can see that the volume of the actual pipe is nothing but the difference of volumes of the two assumed pipes. So, actual volume,
$\Rightarrow V=\left( 1099.557-395.84 \right)c{{m}^{3}}=703.717c{{m}^{3}}$
Thus, we can conclude that the volume of the electric pipe will be $703.717c{{m}^{3}}$ .

Note: We can also solve this problem using another way. The formula for a hollow cylindrical pipe is $V=\pi {{\left( {{r}_{o}}-{{r}_{i}} \right)}^{2}}h$ , where ${{r}_{o}},{{r}_{i}}$ are the external and internal radius respectively. Putting ${{r}_{o}},{{r}_{i}},h$ as $5cm,3cm,14cm$ respectively, we get the answer.