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Answer 1

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 = $\pi r^{2} + 2\pi rh_{c} + 2(lh + wh) + lw-\pi r^{2}$

Where r is the radius of the cylindrical top

$h_{c}$ is the height of the cylindrical top

$l$ is the length of the box

$h$ is the height of the box

$w$ is the width of the box

From the given information,

r = 2 m

$h_{c}$ = 3 m

$l$ = 9 m

$h$ = 2.4 m

$w$ = 5 m

Putting the parameters into the equation, we get

Surface area of the composite solid = $(\pi \times 2^{2} )+ (2\pi \times 2 \times 3) + 2(9\times2.4 + 5\times2.4) + 9\times5-(\pi \times 2^{2} )$

= $(12\pi ) + 2(21.6 + 12) + 45$

= $12\pi + 2(33.6 ) + 45$

= $12\pi +67.2+ 45$

$= 12\pi +112.2$

$= 37.699 +112.2$

$= 149.8991$ 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: brainly.com/question/13175744

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