Question

A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm and radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs. 15 per 100 cm². [use π = 3.14]

Answer 1

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

= (20-8)² + 16²

= 144 + 256

= 400

or l = 20 cm

Now,

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 cm²

(1)⇨

Area of metal sheet used = (πr² + πR² + π(R + r)l) – πR²

= πr² + π(R + r)l

= π(8² + (20 + 8)20)

= 1959.36 cm³

Again,

Cost of 1959.36 cm² metal sheet = 1959.36 × cost of 1 cm² metal sheet

= 1959.36 × Rs. 0.15

= Rs.293.904