Question

The internal and external diameters of a hollow hemispherical vessel are 14 cm and 21 cm, respectively. The cost of silver plating is Rs 0.40 per 1 cm² of surface area. Determine the total cost of silver plating for the entire vessel.

Answer 1

To find the total cost of silver plating a hollow hemispherical vessel, calculate the external and internal surface areas, then find the area to be plated and multiply by the cost per square centimeter.

Step-by-step explanation:

The problem asks us to calculate the total cost of silver plating a hollow hemispherical vessel with given internal and external diameters, and a given rate for silver plating per square centimeter. First, we calculate the internal and external surface areas of the hollow hemisphere, subtract them to get the area to be plated, and then multiply by the cost per square centimeter to obtain the total cost.

Step-by-step solution:

1. Calculate the external surface area of the hemisphere: Aouter = 2πr2, where r is the external radius.
2. Calculate the internal surface area of the hemisphere: Ainner = 2πr2, where r is the internal radius.
3. Compute the surface area to be silver plated: Aplated = Aouter - Ainner.
4. Multiply the area to be plated by the cost per square centimeter to find the total cost: Total Cost = Aplated × Cost per cm2.

Now, calculate each step with the provided dimensions:

• Aouter = 2π(10.5 cm)2
• Ainner = 2π(7 cm)2
• Then, Aplated = Aouter - Ainner
• Finally, Total Cost in Rupees.

After doing the calculations, you will get the total cost for silver plating the entire vessel.