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 surface area of the solid.

From figure,

Radius of cylinder = Radius of hemisphere = r = $\dfrac{\text{diameter}}{2} = \dfrac{7}{2}$ = 3.5 cm

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

= 19 - 2 × 3.5

= 19 - 7

= 12 cm.

Total volume of solid = 2 × Volume of hemisphere + Volume of cylinder

$= 2 \times \dfrac{2}{3} π\text{r}^3 + π\text{r}^2\text{h} \\[1em] = π\text{r}^2 (\dfrac{4}{3} \text{r} + \text{h}) \\[1em] = \dfrac{22}{7} \times 3.5^2 (\dfrac{4}{3} \times 3.5 + 12) \\[1em] = \dfrac{22}{7} \times 12.25 (\dfrac{14}{3} + 12) \\[1em] = \dfrac{269.5}{7} \times \dfrac{14 + 36}{3} \\[1em] = \dfrac{269.5}{7} \times \dfrac{50}{3} \\[1em] = \dfrac{13475}{21} \\[1em] = \dfrac{1925}{3} \\[1em] = 641.67 \text{ cm}^3.$

Surface area of solid = 2 × 2πr² + 2πrh

= πr(4r + 2h)

$= \dfrac{22}{7} \times 3.5 (4 \times 3.5 + 2 \times 12) \\[1em] = 22 \times 0.5 (14 + 24) \\[1em] = 11 \times 38 \\[1em] = 418 \text{ cm}^2.$

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