The number of square meters of paint needed to cover the surface is 149.90m²
Surface area of composite solids
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
To do this, 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_{b} + wh_{b} ) + lw-\pi r^{2}[/tex]
Surface area of the composite solid = [tex]2\pi rh_{c} + 2(lh_{b} + wh_{b} ) + lw[/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_{b}[/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] = 4 m
[tex]h_{b}[/tex] = 2.4 m
[tex]w[/tex] = 5 m
Put the parameters into the equation,
Surface area of the composite solid = [tex](2\pi \times 2 \times 3) + 2(9\times2.4 + 5\times2.4) + 9\times5[/tex]
[tex]= 12\pi +112.2[/tex]
[tex]= 37.699 +112.2[/tex]
[tex]= 149.899[/tex] m²
≅ 149.90 m²
∴ Surface area of the composite solid ≅ 149.90 m²
Hence, the number of square meters of paint needed to cover the surface is 149.90m²
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