Question

A hollow metallic cylinder is made from a metallic sheet of \[2.6cm\] thickness. The outer radius of the cylinder is $3.8cm$ and length is $50cm$ then find the volume of metal.

Answer 1

Hint:Volume of hollow cylinder gives volume of metal so volume of hollow cylinder $V = \pi \times {\left( {{r_1} - {r_2}} \right)^2} \times l$ so here ${r_1}$ is outer radius of the cylinder and ${r_2}$ is inner radius of cylinder and $l$ is length of cylinder.
As we see in this question there is no inner radius so to find inner radius we use a formula that is thickness = outer radius – inner radius or ${r_1} - {r_2}$ .

Complete step-by-step answer:
A hollow metallic cylinder made from a metallic sheet of \[2.6cm\] thickness.
The outer radius of the cylinder is ${r_1} = 3.8cm$ and length $l$ is $50cm$
The volume of metal $V = \pi \times {\left( {{r_1} - {r_2}} \right)^2} \times l$
Now here ${r_2}$ is inner radius
So we find first inner radius
Thickness = outer radius – inner radius or ${r_1} - {r_2}$
$2.6 = 3.8 - {r_2}$
By solving that we get
${r_2} = 1.2cm$
So by putting value of inner radius , outer radius and length we get
So $V = \pi \times {\left( {3.8 - 2.6} \right)^2} \times 50$
Now we know that $\pi = 3.14$
So by solving this we get
$V = 3.14 \times {\left( {1.2} \right)^2} \times 50$
By multiplying all the term we get
$V = 226.68c{m^3}$
Therefore the volume of metallic cylinder is $V = 226.68c{m^3}$

Note:A hollow cylinder is one which is empty from inside and has some difference between the internal and external radius. We see hollow cylinders every day in our day to day lives. Tubes, circular buildings, straws these are all examples of a hollow cylinder.
Lateral Surface Area of a hollow cylinder = $2\pi h({r_1} + {r_2})$
A cylinder is a three-dimensional solid that contains two parallel bases connected by a curved surface. The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.