Question

A bucket made up of a metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs. 20 per litre and the cost of metal sheet used if it costs Rs. 10 per 100cm².

Answer 1

Greater diameter of the bucket = 30 cm

Radius of the bigger end of the bucket = R = 15 cm

Diameter of the smaller end of the bucket = 10 cm

Radius of the smaller end of the bucket = r = 5 cm

Height of the bucket = 24 cm

Slant height, l = √{h² + (R – r)²}

= √{(24)² +(15 – 5)²

= √576 + (10)²

= √576 + 100

= √676

= 26 cm

Now,

= 3.14 × 8 [225 + 25 + 75]

= 3.14 × 8 ×325

= 8164 cm³

= 8.164 Litres

A litre of milk cost Rs 20

So, total cost of filling the bucket with milk = Rs 20 × 8.164

= Rs 163.28

Surface Area of the bucket

= CSA of the frustum + Area of circular base

= πl(R+r) + πr²

= π [{26×(15+5)} + (5)²]

= π[520 + 25 ]

= 3.14 × 545

= 1711.3 cm²

Cost of 100cm² of metal sheet = Rs 10

= Rs 171.13