A solid cylinder has total surface area of 462 sq. cm. Curved surface area is 1/3 rd of it’s total surface area. What is the volume of the cylinder

curved surface area (C S A) is 1/3 rd of its total surface (T S A) area

C S A = $$ \frac{ T S A}{3} $$

$$ C S A = \frac{462}{3} = 154 $$

rest of area = 462 - 154 = 308

base area = $$ 2 \pi r^2 = 308 $$

$$ 2 \times \frac{22}{7} \times r^2 = 308 $$

solving, r = 7

$$ 2 \pi r h = 154 $$

$$ 2 \times \frac{22}{7} \times 7 \times h = 154 $$

solving h = $$ \frac{7}{2} $$

$$ volume = \pi r^2 h $$

               = $$ \frac{22}{7} \times 7^2 \times \frac{7}{2} = 539 $$