Question

The curved surface area of a cylinder is 2200 square cm and circumference of its base is 220 cm. Then the height of cylinder is:
A. 22
B. 10
C. 25
D. 2.2

Answer 1

Hint: We will use the formula of surface area of cylinder and the formula of circumference of its base which is as follows:
Circumference \[=2\pi r\], where r is radius.
Curved surface area \[=2\pi rh\], where r is radius and h is height of the cylinder.

Complete step-by-step solution -
We have been given that the curved surface area of the cylinder is 2200 square cm and circumference of its base is 220 cm.
Now, as we know that the curved surface area of the cylinder is as follows:
Curved surface area \[=2\pi rh\], where r is radius and h is height of the cylinder.
Let us suppose that the radius and the height of the given cylinder to be r and h respectively as shown in the figure.

\[\Rightarrow 2\pi rh=2200....(1)\]
We also know that the circumference of the circular base \[=2\pi r\]
\[\Rightarrow 2\pi r=220.....(2)\]
Now substituting the value of \[g\left( 2\pi r \right)\] from equation (2) in equation (1) we get as follows:
\[\Rightarrow 220\times h=2200\]
On dividing the equation by 220 we get as follows:
\[\begin{align}
  & \dfrac{220h}{220}=\dfrac{2200}{220} \\
 & \Rightarrow h=10cm \\
\end{align}\]
Hence the height of the cylinder is equal to 10 cm.
Therefore, the correct answer option of the above question is option B.

Note: Take care of the unit of variable. Also remember that the curved surface area of an object is the area of all the curved surface area of the object, we can’t include the flat surface area of the object. If we include it then it would become lateral surface area.