In given problem a bucket made up of a metal sheet is in the form of a frustum of a cone. To find answer of this question use pathogroups theorem.
Problem from RS Aggarwal book, problem number 8, page number 823, exercise 17C, chapter volume and surface area of solid.
Chapter Mensuration
Solution
given data
Radius of lower circular end = r = 8 cm
Radius of upper circular end = R = 20 cm
Height of container frustum = h = 16 cm
Cost of 100 cm2 metal sheet = rs. 15
Cost of 1 cm2 metal sheet = 15/100 = Rs. 0.15
Slant height,
l2 = (R-r)2 + h2
l2 = (20-8)2 + 162
l2 = 144 + 256
l2 = 400
l = 20 cm
Area of metal sheet used = (Total surface area of frustum)- (Area of upper circle) …(1)
Area of upper circle = πR2
Total surface area of frustum = πr2 + πR2 + π(R + r)l
Area of metal sheet used = (πr2 + πR2 + π(R + r)l) – πR2
= πr2 + π(R + r)l
= π(82 + (20 + 8)20)
Area of metal sheet used = 1959.36 cm3
Cost of 1959.36 cm2 metal sheet = 1959.36 × cost of 1 cm2 metal sheet
= 1959.36 × Rs. 0.15
∴ cost of the bucket if the cost of metal sheet used is Rs. 15 per 100 cm² is Rs.293.904