If the base area of a right circular cylinder is $$346.50 cm^2$$ and its height is 21 cm , then find its total surface area. [Use $$\pi = \frac{22}{7}$$​]

Correct option is C

Given:

The base area of the right circular cylinder is = 346.50

The height of the cylinder is = 21 cm

Use π= $$\frac{22}{7}$$​​

Formula Used:

The base area of a right circular cylinder is given by the formula:

​$$A_{\text{base}} = \pi r^2$$​​

The total surface area of a cylinder is given by:  $$A_{\text{total}} = 2\pi r^2 + 2\pi rh$$​​

Solution: ​

From the base area formula;

πr² = $$346.50$$ 

​$$\frac{22}{7} r^2$$​ = 346.50

​$$22 r^2 = 346.50 \times 7$$ = 2425.50 

​$$r^2 = \frac{2425.50}{22}$$ = 110.25 

r = 110.25 = 10.5cm  

Now, total surface area: 

​$$A_{\text{total}} = 2\pi r^2 + 2\pi rh$$ 

Now, 

​​​​$$2\pi r^2 = 2 \times \frac{22}{7} \times (10.5)^2 \\ \ \\ = 2 \times \frac{22}{7} \times 110.25\\ \ \\ = 2 \times 346.50 = 693 \, \text{cm}^2$$ 

and 

​$$2\pi rh = 2 \times \frac{22}{7} \times 10.5 \times 21 \\ \ \\ = 2 \times \frac{22}{7} \times 220.5 \\ \ \\ = 1386 \, \text{cm}^2$$ 

Thus, 

$$A_{\text{total}} = 693 + 1386 = 2079 \, \text{cm}^2$$​