A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and the total surface area of the solid.

From figure,

r = Radius of cylinder = Radius of hemisphere = $\dfrac{7}{2}$.

Height of cylinder (h) = Total height - (2 x Radius of hemisphere)

= 19 - $\Big(2 \times \dfrac{7}{2}\Big)$

= 19 - 7 = 12 cm.

Total Volume of solid (V) = 2 × Volume of hemisphere + Volume of cylinder

$\therefore V = 2 \times \dfrac{2}{3}πr^3 + πr^2h \\[1em] = πr^2\Big(\dfrac{4r}{3} + h\Big) \\[1em] = \dfrac{22}{7} \times \dfrac{7}{2} \times \dfrac{7}{2} \Big(\dfrac{4}{3} \times \dfrac{7}{2} + 12\Big) \\[1em] = \dfrac{11 \times 7}{2} \times \Big(\dfrac{14}{3} + 12\Big) \\[1em] = \dfrac{77}{2} \times \Big(\dfrac{14}{3} + 12\Big) \\[1em] = \dfrac{77}{2} \times \dfrac{14}{3} + \dfrac{77}{2} \times 12 \\[1em] = \dfrac{539}{3} + 462 \\[1em] = \dfrac{539 + 1386}{3} \\[1em] = \dfrac{1925}{3} \\[1em] = 641\dfrac{2}{3} \text{ cm}^3.$

Surface area of solid (S) = 2 × Surface area of each hemisphere + Surface area of cylinder.

$\therefore S = 2 \times 2πr^2 + 2πrh \\[1em] = πr(4r + 2h) \\[1em] = \dfrac{22}{7} \times \dfrac{7}{2} \times \Big(4 \times \dfrac{7}{2} + 2 \times 12\Big) \\[1em] = 11 \times (14 + 24) \\[1em] = 11 \times 38 \\[1em] = 418 \text{ cm}^2$

Hence, the volume of the solid = $641\dfrac{2}{3}$ cm³ and surface area of solid = 418 cm².