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

Answer 1

is it right i am not sure

Answer 2

Answer-

The height of the vessel is 10m.

Solution-

If the total cost of painting the outer curved surface of the vessel is 352 rupees at the rate of 0.2 per 100 cm²

i.e 0.2 rupees is spent for painting 100 cm², so calculation for 252 will be give us the area.

Area of the curved surface, will be

$=\frac{100\times 352}{0.2} =176,000\ cm^2$

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,

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

$A=175.93h$

This two expression for area will be same,

$\Rightarrow 175.93h=176,000$

$\Rightarrow h=\frac{176,000}{175.93}=1000.39\approx 1000\ cm$

$\Rightarrow h=10\ m$

Therefore, the height of the vessel is 10m