Problem 3
If we peel off the sticker off the side of a 3D cylinder, then we can form a rectangle (imagine we're able to peel it off completely without any folds or tears).
The length of the rectangular sticker is the distance around the curved circular base. So it's C = pi*d = pi*1.5 = 1.5pi inches across. The height of the rectangle is the same as the height of the cylinder. So the height is 5 inches.
The area of the rectangle is: length*width = (1.5pi)*(5) = 7.5pi
That's the exact area in terms of pi
If you use the approximation pi = 3.14, then we'll get 7.5*3.14 = 23.55 square inches as the final answer
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Problem 4
The square base has area of 38*38 = 1444 square cm
The side panels are 4 identical triangles. Each triangle has area base*height/2 = 38*55/2 = 1045 square cm. Meaning that all four triangles combine to a lateral surface area of 4*1045 = 4180 sq cm.
The total surface area is: 1444+4180 = 5624 square cm.
When you wrote 55*38*2+38*38 on your paper, you had the right idea because that evaluates to 5624
