Question

Find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. Given that the width of the metal sheet is 1 m. Also, find the cost of the sheet at the rate of Rs. 56 per m.

Find the area of metal sheet required, if 10% of it is wasted in cutting, overlapping, etc.

Answer 1

Height of the cylindrical box = h = 35 cm

Base radius of the cylindrical box = r = 10 cm

Width of metal sheet = 1 m = 100 cm

Area of metal sheet required = Total surface area of the box 

`=>` Length × width = 2πr(r + h)

`=>` Length × 100 = `2 xx 22/7 xx 10(10 + 35) `

`=>` Length × 100 = `2 xx 22/7 xx 10 xx 45`

`=>` Length = `(2 xx 22 xx 10 xx 45)/(100 xx 7)` = 28.28 cm = 28 cm

∴ Area of metal sheet = Length × Width

= 28 × 100

= 2800 cm²

= 0.28 m² 

∴ Cost of the sheet at the rate of Rs. 56 per m²

= Rs. (56 × 0.28)

= Rs. 15.68

Let the total sheet required be x.

Then, x – 10% of x = 2800 cm² 

`=> x - 10/100 xx x = 2800`

`=> (10x - x)/10 = 2800`

`=> (9x)/10 = 2800`

`=>x = (2800 xx 10)/9`

`=>` x = 3111 cm²