A solid metal sphere is cut through its center into 2 equal parts. If the diameter of the sphere is $3\dfrac{1}{2}$ cm, find the total surface area of each part correct to two decimal places.

Diameter of sphere = $3\dfrac{1}{2} = \dfrac{7}{2}$ cm.

Radius of sphere (r) = $\dfrac{\dfrac{7}{2}}{2} = \dfrac{7}{4}$ cm.

Total surface area of each hemisphere = $\dfrac{1}{2}$ Curved surface area of sphere + Area of circular base

= $\dfrac{1}{2} \times 4πr^2 + πr^2$

= 2πr² + πr²

= 3πr²

$= 3 \times \dfrac{22}{7} \times \dfrac{7}{4} \times \dfrac{7}{4} \\[1em] = 3 \times \dfrac{22 \times 7}{16} \\[1em] = 3 \times \dfrac{77}{8} \\[1em] = 28.88 \text{ cm}^2.$

Hence, total surface area of each hemisphere 28.88 cm².