Question

The curved surface area of a right circular cylinder of height 14 cm is $88c{{m}^{2}}$. Find the diameter of the base of the cylinder.

Answer 1

Hint: First, before proceeding for this, we must draw the cylinder figure with height 14 cm and radius r. Then, we know that the curved surface area A of the right circular cylinder with radius r and height h is given by the formula as $A=2\pi rh$. Then, we know one other condition that diameter d is twice the radius r of the circular base and by using it we get the final result.

Complete step by step answer:
In this question, we are supposed to find the diameter of the base of the cylinder when the curved surface area of a right circular cylinder of height 14 cm is $88c{{m}^{2}}$.
So, before proceeding for this, we must draw the cylinder figure with height 14 cm and radius r as:

Then, we know that the curved surface area A of the right circular cylinder with radius r and height h is given by the formula as:
$A=2\pi rh$
Then, by substituting the value of h as 14 cm and A as $88c{{m}^{2}}$, we get the value of r as:
$88=2\times \dfrac{22}{7}\times r\times 14$
Then , by solving the above expression, we get the value of r as:
$\begin{align}
  & 88=2\times 22\times r\times 2 \\
 & \Rightarrow 88=88r \\
 & \Rightarrow r=\dfrac{88}{88} \\
 & \Rightarrow r=1 \\
\end{align}$
So, we get the value of the radius of the cylinder as 1 cm.
Now, we know one other condition that diameter d is the twice of the radius r of the circular base.
Then, by using the above condition, we get the value of diameter d of circular base of cylinder as:
$d=2r$
Then, by substituting the value of r as 1 as calculated above, we get:
$\begin{align}
  & d=2\times 1 \\
 & \Rightarrow d=2cm \\
\end{align}$
Hence, the diameter of the base of the cylinder is 2 cm.

Note:
Now, to solve these types of questions we need to be careful between the two formulas of the cylinder which is CSA(curved surface area) and TSA(total surface area) as these two are different and must not be mixed. So, the formulas for the two for cylinder are as:
The CSA of cylinder with radius r and height h is $2\pi rh$.
TSA of cylinder with radius r and height h is $2\pi r\left( h+r \right)$.