Question

A cylindrical vessel open at the top has a base diameter 56 cm. If the total cost of painting the outer curved surface of the vessel is ` 352 at the rate of ` 0.2 per 100 cm2, then the height of the vessel is (1)15 m(2)10 m (3)6 m(4)12 m

Answer 1

Cost=Rate x Area

352=0.2/100 x 2πrH

352=2/1000 x 2 x 22/7 x 28 x H

352 x 1000 x 7/2 x 2 x 22 x 28 = H

H=1000 cm

H=10 m

Answer 2

Answer-

The height of the vessel is 10m.

Solution-

The diameter of cylindrical vessel = 56 cm, let us assume the height is h cm

Curved surface area of the cylinder is,

$A=\pi \times d\times h$

Putting the values,

$A=\pi \times 56\times h$

$A=175.93h$

The surface was painted at a rate of 0.2 rupees per 100 cm²

Or 100 cm² costs 0.2 rupees, so 175.93h cm² will cost,

$=\frac{0.2\times 175.93h}{100} =0.3519h$

But according to the question, 352 rupees was spent, so

$\Rightarrow 0.3519h=352$

$\Rightarrow h=\frac{352}{0.3519}$

$\Rightarrow h=923.5$

Therefore, the height of cylinder is 923.5 cm or 9.23m or approximately 10m