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Answer :
Jacob's estimate of the shoe box's surface area is reasonable, as the actual calculated surface area is 2706.8 cm², which is very close to his estimate of 2,800 cm².
To determine if Jacob's estimate of the surface area of a shoe box is reasonable, we need to calculate the actual surface area of the rectangular prism. The surface area (SA) of a rectangular prism is given by the formula SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism. In this case, the shoe box has dimensions of 39.4 cm (length), 17.8 cm (width), and 11.4 cm (height).
Let's perform the calculation:
- SA = 2(39.4 x 17.8) + 2(39.4 x 11.4) + 2(17.8 x 11.4)
- SA = 2(701.32) + 2(449.16) + 2(202.92)
- SA = 1402.64 + 898.32 + 405.84
- SA = 2706.8 cm²
Jacob estimated the surface area to be about 2,800 cm², which is quite close to our calculated surface area of 2706.8 cm². Therefore, Jacob's estimate is reasonable.
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