9514 1404 393
Answer:
A is smaller
Step-by-step explanation:
The surface area of a cylinder is ...
A = 2πr² +2πrh = 2πr(r+h)
Here, we have r=30 mm, h = 240 mm, so the surface area is ...
A = 2π(30 mm)(30 +240 mm) = 60,200π mm² ≈ 50,894 mm²
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The box is 2 diameters square and 1 diameter high. Its surface area is ...
A = 2(LW +H(L+W)) = 2((120 mm)(120 mm) +(60 mm)(120 +120 mm))
A = 2(14400 mm² +14400 mm²) = 57,600 mm²
Comparing the two areas, we conclude that ...
A is smaller
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Alternate solution
Since r = d/2, the area of the cylinder is ...
A = 2π(d/2)(d/2 +4d) = 9πd²/2 ≈ 14.14d²
The area of the box is ...
A = 2((2d)(2d) +d(2d +2d)) = d²(2(4 +4)) = 16d²
Then 14.14 < 16, so A is smaller.
