Question

A gap 2 m deep has the shape of a truncated pyramid with rectangular bases. The length and width of the top base is 3x1.5 m and of the bottom base it is 1x0.5 m. To paint one square meter of a gap surface we need 0.25 liters, of a green paint color, How many liters of the paint color, we will need, if we want to paint just the side walls and the bottom base of the gap? Show working please.

Answer 1

Volume of paint required is 3.125 litres.

Explanation:

It would be noted that each side walls would have the shape of a trapezium. So that the areas of each wall can be determined as:

wall 1 =
`(1)/(2)`(a + b) h

=
`(1)/(2)`(0.5 + 1.5)2

= 2
`m^(2)`

wall 2 =
`(1)/(2)`(a + b) h

=
`(1)/(2)`(1 + 3)2

= 4
`m^(2)`

wall 3 =
`(1)/(2)`(a + b) h

=
`(1)/(2)`(0.5 + 1.5)2

= 2
`m^(2)`

wall 4 =
`(1)/(2)`(a + b) h

=
`(1)/(2)`(1 + 3)2

= 4
`m^(2)`

Total area of the walls = 2 + 2 + 4 + 4

= 12
`m^(2)`

Area of the bottom base = l x b

= 1 x 0.5

= 0.5
`m^(2)`

Total area to be painted = 12 + 0.5

= 12.5
`m^(2)`

But to paint one square meter of a gap surface, we need 0.25 litres of a green paint color. Thus, to paint 12.5
`m^(2)` of the gap surface:

12.5 x 0.25 = 3.125

The litres of paint required is 3.125.