A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase in its total surface area?

77 cm²

We have,

Diameter = 7

Then the radius (r) = \(\frac{7}{2}\) = 3.5

Initial surface area = 4πr² = 4 π (3.5)²

Final surface area = 4πr² + 2 π r²

Final surface area = 6πr²

Increase in total surface area = 6πr² - 4πr² = 2πr²

Increase in total surface area = 2π(3.5)² = 2 × \(\frac{7}{2}\) × (3.5)² = 76.96 = 77cm²