The respective ratio between numerical values of the curved surface area and the volume of a right circular cylinder is 2 : 3. If the respective ratio between the radius and the height of the cylinder is 3 : 7, what is the total surface area of the cylinder?

Correct option is B

Given:
Ratio between radius and height = 3 : 7
Let radius be 3x and height be 7x.
Ratio between curved surface area and volume of cylinder = 2 : 3
Formula Used:
Curved surface area of cylinder =2πrh
Volume of the cylinder = $$πr^2 h$$​​
Solution:
As per the question,
​$$\frac{2πrh}{(πr^2 h)}=\frac{2}{3} \\\ \\\frac{(2×π×r×h)}{(π×r^2×h)}=\frac{2}{3}\\\ \\\frac{(2×π×3x×7x)}{(π×3x×3x×7x)}=\frac{2}{3} \\\ \\\frac{2}{3x}=\frac{2}{3}\\\ \\x = 1$$​​
Then,
Radius, r = 3×1 = 3cm, height h = 7×1 = 7cm
Now,
Total surface area of cylinder =2πr(r+h)
= 2×π×3(3+7)
= 60π cm$$^2$$​​