The radius of a solid right circular cylinder is $$66\frac{2}{3}\%$$ of its height. If the height is 'h' centimeters then its total surface area(in $$cm^2$$)is:

If the height of a solid right circular cylinder is 'h' cm.

Let's assume the radius of a solid right circular cylinder is 'r' cm.

The radius of a solid right circular cylinder is $$66\frac{2}{3}\%$$ of its height.

r = $$66\frac{2}{3}\%$$ of h

$$r=\frac{2h}{3}$$    Eq.(i)

Total surface area = $$2\pi\ r\left(r+h\right)$$

Put Eq.(i) in the above formula.

= $$2 \pi \times \frac{2h}{3}(\frac{2h}{3}+h)$$

= $$2\pi\times\frac{2h}{3}\times\ \frac{5h}{3}$$

= $$\frac{20}{9}\pi h^2$$