The curved surface area of a cylindrical pillar is 66 $$\text{m}^2$$​ and its volume is 231 $$\text{m}^3$$​. Find the measure of its radius.

(Take π = $$\frac{22}{7}$$​)

Correct option is B

Given:
Curved Surface Area (CSA) of the cylindrical pillar = 66 $$\, \text{m}^2 .$$​
Volume of the cylindrical pillar = 23$$1 \, \text{m}^3 .$$​
​$$\pi = \frac{22}{7}$$​​
Formula Used:
Curved Surface Area (CSA) of a cylinder = $$= 2\pi r h$$​​
​​Volume of a cylinder = $$= \pi r^2 h$$​​
where r = radius and  h = height.
Solution:
​$$2\pi r h = 66$$​
​$$2 \times \frac{22}{7} \times r \times h = 66$$​
​$$\frac{44}{7} r h = 66$$​

​$$r h = \frac{66 \times 7}{44} = \frac{462}{44} = 10.5$$​

​$$h = \frac{10.5}{r}$$​
Also:
​$$\pi r^2 h = 231 \\ \ \\\frac{22}{7} \times r^2 \times \frac{10.5}{r} = 231 \\ \ \\\frac{22}{7} \times r \times 10.5 = 231 \\ \ \\22 \times r \times 1.5 = 231 \quad \left( \text{Since} \frac{10.5}{7} = 1.5 \right) \\ \ \\33 r = 231 \\ \ \\r = \frac{231}{33} = 7$$​​
The radius of the cylindrical pillar is 7 m.