Question

A vessel without a lid has the shape of a cylinder. The height of the vessel is 1.5 m, and the diameter of the base represents 40% of the height. Determine if 1 kg of paint is enough to completely paint the vessel inside and out, if it is known that for 1 square meter of surface 150g of paint is consumed.​

Answer 1

Answer:

Yes, 1 kg of paint is enough to completely paint the inside and outside surfaces of the vessel.

Step-by-step explanation:

For the given vessel without a lid,

diameter = 0.4 x 1.5

               = 0.6 m

radius = $\frac{diameter}{2}$ = $\frac{0.6}{2}$

           = 0.3 m

Total external surface area of the vessel = 2$\pi$rh + $\pi$$r^{2}$

                             = [2 x $\frac{22}{7}$ x 0.3 x 1.5] + [$\frac{22}{7}$ x $(0.3)^{2}$]

                             = 2.8286 + 0.2829

                             = 3.1112

Total external surface area of the vessel is 3.1112 square meter.

Total internal and external surface area = 2 x 3.1112

                                                              = 6.2224 $m^{2}$

But for 1 square meter, 150 g of paint is consumed. Thus;

for 6.2224 $m^{2}$ = 6.2224 x 150 g

                       = 933.36 g

Thus, 6.2224 $m^{2}$ of area would require 933.36 g of paint.

So that,

$\frac{933.36}{1000}$ = 0.93336 kg

Therefore, 1 kg of paint is enough to completely paint the inside and outside surfaces of the vessel.