Question

A solid trophy, consisting of two parts, has been designed in the following manner: the bottom part is a frustum of a cone with the bottom radius 30 cm, the top radius 20 cm, and height 40 cm, while the top part is a hemisphere with radius 20 cm. Moreover, the flat surface of the hemisphere is the same as the top surface of the frustum. If the entire trophy is to be gold-plated at the cost of Rs. 40 per square cm, what would the cost for gold-plating be closest to?

• A. Rs. 3,60,000
• B. Rs. 3,72,000
• C. Rs. 1,12,000
• D. Rs. 5,23,000
• E. Rs. 4,73,000

Hint:

For composite shapes, calculate the surface area of each part separately and then sum them up for the total area.

Answer 1

The Correct Option is B

Step 1: Calculate the surface areas of the frustum and hemisphere.
Use the standard formulae to determine the surface area of the frustum and the hemisphere.
Step 2: Sum the surface areas and apply the cost per square cm.
Multiply the combined surface area by the given rate of Rs. 40 per square cm.
Final Answer: \[\boxed{\text{Rs. 3,72,000}}\]