Question

The curved surface area of a cylinder is $176\,\,c{m^2}$ and its base area $38.5\,\,c{m^2}$ .Find the volume of the cylinder and justify your answer.

Answer 1

Hint:
If r be the radius of the circular base and h be the height of the cylinder, then the volume is. $\pi {r^2}h$. And the curved surface area is $2\pi rh$ and base area is $\pi {r^2}$.

Complete step by step solution:
Step1:Since, the curved surface area of the cylinder is $176\,\,c{m^2}$ then
                                  $2\pi rh = 176$ …………….(1)

Step2:The base area is $38.5\,\,c{m^2}$ ,then
                                 $\pi {r^2} = 38.5$ ……………..(2)

Step3:From equation (1),
                                  $r = \dfrac{{176}}{{2\pi h}}$ ……………………(3)

Step4:Putting this value of r into (2),
                                    $\eqalign{
  & \pi {\left( {\dfrac{{176}}{{2\pi h}}} \right)^2} = 38.5 \cr
  & or, {h^2} = \dfrac{{{{88}^2}}}{{\pi \times 38.5}} = 64.026(approx) \cr
  & or, h = 8.002(approx) \cr} $
Step5:Then the volume of the cylinder will be
$\eqalign{
  & = \pi {r^2}h \cr
  & = 38.5 \times 8.002 \cr
  & = 308.08\,\,c{m^3}(approx.) \cr} $
Here the volume of the cylinder is $308.8\,\,c{m^3}$. Approximately.

Note:
If we check for the circular base radius r,put the value of h in equation (3). Then ..$r = \dfrac{{176}}{{2\pi \times 8.002}} = 3.5\,\,cm(approx.)$.