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

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

Explanation:

For the given vessel without a lid,

diameter = 0.4 x 1.5

= 0.6 m

radius =
`(diameter)/(2)` =
`(0.6)/(2)`

= 0.3 m

Total external surface area of the vessel = 2
`\pi`rh +
`\pi`
`r^(2)`

= [2 x
`(22)/(7)` x 0.3 x 1.5] + [
`(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,

`(933.36)/(1000)` = 0.93336 kg

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