Answer:
[tex]\boxed {616 \ cm^2}[/tex]
Step-by-step explanation:
Curved surface area of the cylinder can be calculated by using the formula,
To calculate the Curved surface area of the cylinder, first we need to know the radius of the cylinder.
Given that :-
Volume of the cylinder can be calculated by using the formula, Volume of cylinder = πr²h.
On substituting the required values in the above formula, we will get the value of the radius.
substituting the required values, we have:
[tex] \sf 2156 = \dfrac{22}{7} \times r^2 \times 14 [/tex]
[tex] \sf 2156 = r^2 \times 154 [/tex]
dividing both sides by 154,
[tex]\sf 14 = r^2 [/tex]
squaring both sides,
[tex] {\pmb{\sf{r = 7 \: cm}}}[/tex]
Now we can calculate the Curved surface area of the cylinder:
Substituting the required values, we have:
[tex] \sf {CSA} = 2 \times \dfrac{22}{7} \times 7 \times 14[/tex]
[tex]\sf {CSA} = 2 \times 22 \times 14 [/tex]
[tex]\sf {CSA} = 44 \times 14 [/tex]
[tex]{\boxed{\pmb{\sf {CSA = 616\: cm^2}}}} [/tex]
Therefore, the Curved surface area of the cylinder is 616 cm²
