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 cm

^{2}metal sheet = rs. 15Cost of 1 cm

^{2}metal sheet = 15/100 = Rs. 0.15Slant height,

l

^{2}= (R-r)^{2}+ h^{2}l

^{2 }= (20-8)^{2}+ 16^{2}l

^{2 }= 144 + 256l

^{2 }= 400l = 20 cm

Area of metal sheet used = (Total surface area of frustum)- (Area of upper circle) …(1)

Area of upper circle = πR

^{2}Total surface area of frustum = πr

^{2}+ πR^{2}+ π(R + r)lArea of metal sheet used = (πr

^{2}+ πR^{2}+ π(R + r)l) – πR^{2}= πr

^{2}+ π(R + r)l= π(8

^{2}+ (20 + 8)20)Area of metal sheet used = 1959.36 cm

^{3}Cost of 1959.36 cm

^{2}metal sheet = 1959.36 × cost of 1 cm^{2}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