Abhi has a solid sphere of diameter 10 cm. He cuts it into two equal halves and decides to paint it. The painting cost per square cm is Rs.10. Which of the following is the approximate difference between the painting cost of the sphere and the hemispheres? (Use π = 22/7, rounded off to two decimal places.)

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 02 Feb 2023 Shift 3)

Answer 1

Given:

Diameter of the sphere = 10 cm

Cost per sq cm = Rs. 10

Concept:

Surface area of sphere = 4πr²

Surface area of hemisphere = 2πr²

Solution:

The difference in the painting costs = (2 × Total Surface area of hemisphere - Surface area of sphere) × Cost per sq cm

⇒ Difference = (2 × 3πr² - 4πr²) × Rs.10

⇒ Difference = 2πr2 × Rs.10

⇒ Difference = 2 × 22/7 × 5 × 5 × Rs.10 = Rs.1,571.43

Therefore, difference in the painting cost between the sphere and the hemispheres is Rs.1,571.43.