Answer:
340 in²
Step-by-step explanation:
The total surface area of the composite figure can be considered to be the sum of the surface area of the rectangular prism base and the lateral surface area of the cylinder. Effectively, the hidden area at the interface between the two shapes is translated to the top of the cylinder, where it is visible again.
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prism area
The area of a rectangular prism is given by the formula ...
A = 2(LW +H(L +W))
Using the given dimensions, we find the area of the rectangular prism base to be ...
A = 2((9 in)(9 in) +(3 in)(9 in +9 in)) = 2(81 +3(18)) in² = 270 in²
Since the bottom area will not be painted, we can subtract its area of 81 in².
prism area = 270 in² -81 in² = 189 in²
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cylinder area
The lateral area of the cylinder is the product of its circumference and height.
A = 2πrh
A = 2(3.14)(4 in)(6 in) = 150.72 in² . . . . lateral area
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total surface area
The painted area is the sum of the areas just computed:
painted area = prism area + cylinder area
= 189 in² +150.72 in² = 339.72 in² ≈ 340 in²
To the nearest square inch, the amount of paint needed is that required to cover an area of 340 in².
