The adjoining figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other end. Given that, common radius = 3.5 cm, the height of the cylinder = 6.5 cm and the total height = 12.8 cm, calculate the volume of the solid, correct to the nearest integer.

Given, common radius, r = 3.5 cm

Height of cylinder, H = 6.5 cm

Height of hemisphere = radius of hemisphere = 3.5 cm

Height of cone, h = Total height of the solid - height of cylinder - height of hemisphere = 12.8 - 6.5 - 3.5 = 2.8 cm

Volume of solid = Volume of cone + Volume of cylinder + Volume of hemisphere

$= \dfrac{1}{3} π\text{r}^2\text{h} + π\text{r}^2\text{H} + \dfrac{2}{3} π\text{r}^3 \\[1em] = π\text{r}^2 \Big(\dfrac{1}{3} \text{h} + \text{H} + \dfrac{2}{3} \text{r}\Big) \\[1em] = \dfrac{22}{7} \times (3.5)^2 \times \Big(\dfrac{1}{3} \times 2.8 + 6.5 + \dfrac{2}{3} \times 3.5 \Big) \\[1em] = \dfrac{22}{7} \times 12.25 \times \Big(\dfrac{2.8}{3} + 6.5 + \dfrac{7}{3} \Big) \\[1em] = 22 \times 1.75 \times \Big(\dfrac{2.8 + 19.5 + 7}{3} \Big) \\[1em] = 38.5 \times \dfrac{29.3}{3} \\[1em] = \dfrac{1128.05}{3} \\[1em] = 376.02 \approx 376 \text{ cm}^3.$

Hence, volume of solid is 376 cm³.