A solid cylinder of diameter 50 cm and height 75 cm needs to be chrome-plated at all the surfaces, if the cost of chrome plating is Rs. 1 per cm² find the total cost of chrome plating. Assume π = 3.14

Concept:

Total surface area of a cylinder = (Area of the curved surface) +  (Area of top and base circles of the cylinder)

\(A=(\pi DL)+\frac{\pi D^2}{4}+\frac{\pi D^2}{4}\)

\(A=(\pi DL)+\frac{\pi D^2}{2}\)

where R = radius of cylinder, L = length of cylinder

Total Cost = (cost of plating of 1 cm² area) × (total surface area)

Calculation:

Given:

D = 50 cm, L = 75 cm, cost of plating = Rs. 1 /cm²

\(A=(\pi×50×75)+\frac{\pi×(50)^2}{2}\)

A = 11780.97 + 3926.99

A = 15707.96 cm²

Total cost = 1 × 15707.96

Total cost = Rs. 15707.96

Hence the cost of chrome plating will be Rs. 15707.