Question

A bucket open at the top and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs. 10 per 100 .cm³(use π = 3.14)

Answer 1

Given, 

h = 24 cm, r’ = 15 cm and r’’ = 5 cm 

Let slant height be l 

Slant height, l = \(\sqrt{(r' - r")^2 + h^2}\)

⇒ l = \(\sqrt{(15 - 5)^2 + 24^2}\)

⇒ l = 26 cm 

Total surface area of the frustum = π(r’ + r’’)l+ πr’’² 

= π(15 + 5)(26) + π (5)² 

= 1711.3 cm² 

Cost of metal sheet used at the rate of Rs. 10 per 100 cm² 

= \(\frac{1711.3}{100}\times10\)

= Rs 171