Question

A cylindrical vessel open at the top has a base diameter 56cm .If the total cost of painting the outer curved surface of the vessel is rupees 352 at the rate of rupees 0.2 per 100 cm square then the height of the vessel is

Answer 1

For each 100cm^2=0.2

For each x cm^2=352/0.2 ×10

=1760

Perimeter of cylinderical vessel = πr(2h+r)

1760 = 22/7×28×(2×h+28)

1760 = 44(2h+28)

1760/44=2h+28

40-28=2h

12/2=h

6cm= h

Answer 2

Find the curved surface area:

Rs 0.20 = 100 cm²

Rs 1 = 100 ÷ 0.2 = 500 cm²

Rs 352 - 500 x 352 = 176,000 cm²

Find the radius:

Radius = Diameter ÷ 2

Radius = 56 ÷ 2 = 28 cm

Find the height:

Curved Surface Area = 2πrh

2π(28)h = 176,000 cm²

h = 176,000 ÷ 56π

h = 1000 cm

Answer: The height of the vessel is 1000 cm