Question

Curved surface area of a right circular cylinder is \[4.4{{\text{m}}^2}\]. If the radius of the base of the cylinder is 0.7m, find its height.

Answer 1

Hint: First draw the diagram for better analysis. Look at the parameters given and the parameter that is to be found. Curved surface area and radius is given. Using the formula for curved surface area, height can be found easily.

Complete step by step answer:
Let the height of the circular cylinder be \[h\].
Radius of the base of cylinder \[r = 0.7{\text{m}}\]

Given Curved surface area of cylinder \[S = 2\pi rh = 4.4{{\text{m}}^2}\]
By substituting the above values, we have
\[
   \Rightarrow 2\pi rh = 4.4 \\
   \Rightarrow 2\pi \left( {0.7} \right)h = 4.4 \\
   \Rightarrow 2 \times \dfrac{{22}}{7} \times \left( {0.7} \right)h = 4.4 \\
\]
By cancelation, we have
\[
   \Rightarrow 2\left( {0.1} \right) \times 22h = 4.4 \\
   \Rightarrow 4.4h = 4.4 \\
  \therefore h = \dfrac{{4.4}}{{4.4}} = 1{\text{m}} \\
\]

Therefore, the height of the cylinder is 1m.

Note: Whenever we face such types of problems the key concept that we need to have is the good gist of basic conic section formulas like that of curved surface area being used above. This concept will help to get on the right track to reach the answer.