The total surface area of a hemisphere is 4,158 $$m^2$$​. If the radius of the hemisphere becomes one-third of itself, then what will be the new curved surface area of the hemisphere? (Use π=22/7 )

Correct option is A

Given
Total Surface Area (TSA) of hemisphere = $$4158 m^2$$​​
New radius (r') = $$\frac{1}{3}$$​ of original radius (r)
​$$\pi = \frac{22}{7}$$​​

Formula Used
TSA of a hemisphere = $$3\pi r^2$$  ​
Curved Surface Area (CSA) of a hemisphere = $$2\pi r^2$$​​

Solution
First, find the value of  $$\pi r^2$$​from the TSA:
​$$3\pi r^2 = 4158\\\ \\\pi r^2 = \frac{4158}{3} = 1386$$​​
The new radius is r' = $$\frac{r}{3}.$$​​
New CSA =  $$2\pi (r')^2$$​​
New CSA = $$2\pi (\frac{r}{3})^2 = 2\pi (\frac{r^2}{9})$$​​
New CSA = $$\frac{2}{9} \times (\pi r^2)$$​​
Substitute the value of  $$\pi r^2:$$​​
New CSA = $$\frac{2}{9} \times 1386$$​​
New CSA = $$2 \times 154 = 308 m^2$$​​

Final Answer
So the correct answer is (a)