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 , rounded off to two decimal places.)
Show answer & explanation
Correct answer: C
Explanation
The Correct answer is option 3 i.e.Rs.1,571.43
Given that
Abhi has a solid sphere of diameter 10 cm
The radius = 10/2 = 5 cm
He cuts it into two equal halves and decides to paint it
The painting cost = Rs. 10/cm2
Formula used
The surface area of the sphere = 4πr²
The total surface area of the hemisphere = 3πr²
According to the question
The surface area of the sphere = 4 × (22/7) × 52 = 314.28 cm2
The surface area of the two equal hemisphere = 2 × 3 × (22/7) × 52 = 471.43 cm2
So, the difference of the surface area of the sphere and the two equal hemispheres = 471.43 - 314.28 = 157.15 cm2
Hence, the difference between the painting cost of the sphere and the hemispheres = 157.15 × 10 = Rs. 1571.50