The internal and external diameters of a hollow hemispherical vessel are 28 cm and 32 cm, respectively. The cost incurred to paint 1 cm² of the vessel surface is ₹2.50. Find the total cost incurred to paint the vessel all over, correct to two decimals.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e ₹7574.28.
Total surface area of a hollow hemisphere = Outer curved surface area + Inner curved surface area + Base ring area
Outer curved surface area = 2πR² = 2 × 22/7 × 16² = 2 × 22/7 × 256 = 1609.00 cm²
Inner curved surface area = 2πr² = 2 × 22/7 × 14² = 2 × 22/7 × 196 = 1232.00 cm²
Base ring area = π(R² - r²) = 22/7 × (256 - 196) = 22/7 × 60 = 188.57 cm²
Total surface area = 1609 + 1232 + 188.57 = 3029.57 cm²
Total cost = 3029.57 × 2.50 = ₹7574.28