If a solid sphere is cut into two equal hemispheres, by what percentage is the total surface area increased?
Show answer & explanation
Correct answer: B
Explanation
Given:
Sphere's radius = r
By formula:
Surface area of sphere = 4πr²
Total surface area of hemisphere = 3πr²
Original surface area = 4πr²
When the sphere is cut in two,
Total surface area of the two hemispheres = 2 × 3πr² = 6πr²
Increase in surface area = 6πr² − 4πr² = 2πr²
Percent increase = (2πr² / 4πr²) × 100 = 50%