Question

The internal and external diameters of a hollow hemispherical vessel are 14 cm and 21 cm respectively. The cost of silver plating of 1 cm² surface is ₹ 0.40. Find the total cost of silver plating the vessel all over.

Answer 1

Given:

Internal diameter =14 cm r = 7 cm

External diameter = 21 cm, R = 10.5 cm 

Cost of silver plating = ₹ 0.40 per 1 cm²

To Find:

Total cost of silver plating the vessel all over.

Step:

Find the total surface area to be plated

For a hollow hemispherical vessel, plating “all over” means:

Outer curved area + Inner curved area + Rim (circular ring)

Area = 2πR² + 2πr² + π(R² − r²)

= (2πR² + 2πr² + πR² − πr²)

= 3πR² + πr²

Substitute R = 10.5, r = 7

Area = 3π(10.5)² + π(7)²

= 3π (110.25) + π(49)

= (330.75 π + 49 π) = 379.75 π

Using π = `7/22`

Area = 379.75 × `22/7`

= 54.25 × 22 = 1193.5 cm²

Find the total cost

Cost = 1193.5 × 0.40

= ₹ 477.4