The number of square meters of paint needed to cover the surface is 149.90m²
Surface area of composite solid
From the question, we are to determine the number of square meters of paint needed to cover the surfaces
The number of square meters of paint needed to cover the surfaces is equal to the surface area of the solid
Now, we will calculate the surface area of the composite solid
Surface area of the composite solid = [tex]\pi r^{2} + 2\pi rh_{c} + 2(lh + wh) + lw-\pi r^{2}[/tex]
Where r is the radius of the cylindrical top
[tex]h_{c}[/tex] is the height of the cylindrical top
[tex]l[/tex] is the length of the box
[tex]h[/tex] is the height of the box
[tex]w[/tex] is the width of the box
From the given information,
r = 2 m
[tex]h_{c}[/tex] = 3 m
[tex]l[/tex] = 9 m
[tex]h[/tex] = 2.4 m
[tex]w[/tex] = 5 m
Putting the parameters into the equation, we get
Surface area of the composite solid = [tex](\pi \times 2^{2} )+ (2\pi \times 2 \times 3) + 2(9\times2.4 + 5\times2.4) + 9\times5-(\pi \times 2^{2} )[/tex]
= [tex](12\pi ) + 2(21.6 + 12) + 45[/tex]
= [tex]12\pi + 2(33.6 ) + 45[/tex]
= [tex]12\pi +67.2+ 45[/tex]
[tex]= 12\pi +112.2[/tex]
[tex]= 37.699 +112.2[/tex]
[tex]= 149.8991[/tex] m²
∴ Surface area of the composite solid ≅ 149.90m²
Hence, the number of square meters of paint needed to cover the surface is 149.90m²
Learn more on Calculating surface area of composite solid here: https://brainly.com/question/13175744
#SPJ1
