Question

The curved surface area of a right circular cylinder of height \[14\,cm\]is $ \,\mathop {88\,cm}\nolimits^2 $ . Find diameter of the base of the right circular cylinder.

Answer 1

Hint: Here we have to find the diameter of the base of right circular cylinder so; first we have to find the radius of the right circular cylinder using the formula of surface area of the right circular cylinder. After that we have to calculate the diameter of the right circular cylinder. As we know that the diameter is equal to twice of the radius.

Complete step-by-step answer:
Given that: Curved surface area of a right circular cylinder is $ \,\mathop {88\,cm}\nolimits^2 $ and height of the right circular cylinder is $ 14\,cm $
Therefore, the height of the right circular cylinder is\[14\,cm\].
We know that, Curved surface area of the right circular cylinder $ = 2\pi rh $
And the diameter, $ d = 2 \times Radius $
Here, $ h = $ is the height of the right circular cylinder.
  $ r = $ Radius of base of the right circular cylinder
 $ d = $ Diameter of the right circular cylinder
 So, curved surface area of the right circular cylinder $ 2\pi rh = \mathop {88\,cm}\nolimits^2 $
   $
\Rightarrow 2 \times \dfrac{{22}}{7} \times r \times 14 = 88 \\
\Rightarrow 2 \times 22 \times r \times 2 = 88 \\
  r = \dfrac{{88}}{{2 \times 22 \times 2}} \\
  r = \dfrac{{88}}{{88}} \\
  r = 1\,cm \;
 $
So, diameter of the base of the right circular cylinder
 $ = 2 \times Radius $
       $ = 2 \times 1 $
 $ = 2\,cm $
Hence, the diameter of the base of the right circular cylinder is $ 2\,cm $ .
So, the correct answer is “2 cm”.

Note: The right circular cylinder has two parallel congruent circular bases with a curved rectangle as its sides. The surface area is the areas of all parts needed to cover the object. That is the top, bottom and middle of the object.
Be careful while understanding the word statements and letters, read it twice, do simplification and solve using the mathematical operations.