Question

A cylinder of height $24{\text{ }}cm$ has a curved surface area \[550{\text{ }}c{m^2}\]. Find its volume.

Answer 1

Hint: We are given the height of the cylinder and curved surface area with the help of the curved surface area we will find the radius in it and by substituting the value of radius and height in the formula of volume we get the required volume.

Formula used: Considering the cylinder having height \[h\] and base radius \[r\],
The curved surface area of cylinder is \[2\pi rh\]
Volume of the cylinder is =\[\pi {r^2}h\]

Complete step by step answer:
It is given that, cylinder of height \[24{\text{ }}cm\] has a curved surface area \[550c{m^2}\].

Here, height \[h = 24{\text{ }}cm\]
Radius \[ = r{\text{ }}cm\]
We know the formula for curved surface area of cylinder is \[2\pi rh\] , also given that curved surface area is \[550{\text{ }}c{m^2}\]
From the given data we will find \[r\]
\[2\pi rh = 550\]
Let us substitute the values we know so that we get,
\[2 \times \dfrac{{22}}{7} \times r \times 24 = 550\]
On solving the above equation for \[r\], we get,
\[r = \dfrac{{550 \times 7}}{{24 \times 2 \times 22}} = \dfrac{{5 \times 5 \times 7}}{{24 \times 2}}cm\]
Let us consider the radius of the cylinder as \[\dfrac{{5 \times 5 \times 7}}{{24 \times 2}}cm\]
The formula for finding the volume of the cylinder is \[\pi {r^2}h\]
Let us substitute the values of \[r\] and \[h\] in the volume formula we get,
The volume of the cylinder is
\[\dfrac{{22}}{7} \times \dfrac{{5 \times 5 \times 7}}{{24 \times 2}} \times \dfrac{{5 \times 5 \times 7}}{{24 \times 2}} \times 24\]
On solving the above equation we get the volume as \[1002.60c{m^3}\]
Therefore we have found the volume of the cylinder is \[1002.60c{m^3}\]

Note:
The cylinder is a three-dimensional solid, whose circular base & top are parallel to each other. The perpendicular distance between the top and the base is defined as the total height of the cylinder.
The curved surface area is defined as the area of only curved surfaces, leaving the circular top & base.
We have used the value of $\pi$ to solve the problem, the value of $\pi$ is \[\dfrac{{22}}{7}\] .