Question

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

Answer 1

Diameter of sphere = ${\displaystyle 3\frac{1}{2}cm=\frac{7}{2}cm}$ 

Therefore, radius of sphere = ${\displaystyle \frac{7}{4}cm}$ 

Total curved surface area of each hemispheres = 2πr² + πr²

= 3πr² 

= ${\displaystyle 3\times \frac{22}{7}\times \frac{7}{4}\times \frac{7}{4}}$

= ${\displaystyle \frac{462}{16}c{m}^2}$

= 28.88 cm²