#### Question

A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per

100 cm^{2}

#### Solution

Given that,

The radii of the upper and lower circles of the bucket are r_{1} = 25 cm and r_{2}= 10 cm respectively.

The height of the bucket = 20 cm

The slant height of the bucket

`l=sqrt(h^2+(r_1-r_2)^2`

`=sqrt(20^2+(25-10)^2`

`=sqrt(400+225)`

`=sqrt(625)`

= 25 cm

The surface area of the used aluminium sheet to make the bucket

`S=pi(r_1+r_2)xxl+pir_2^2`

= 3.14(25+10) x 25 + 3.14 x 10 x 10

= 3.14 x 35 x 25 + 3.14 x 100

= 2747.5 + 314

= 3061.5 cm

It is given that the cost of aluminium sheet is Rs 70 per 100 cm^{2}

therefore, the total cost of making the bucket

`Rs 3061.5/100xx70`

Rs 2143.05

Hence, the total cost of making the bucket is Rs 2143.05.