A shoe box is shaped like a rectangular prism. It is 39.4 centimeters long, 17.8 centimeters wide, and 11.4 centimeters tall. Jacob estimates that the surface area of the shoe box is about 2,800 square centimeters. Is his estimate reasonable?

Question

28-06-2024
Mathematics

High School

Thank you for visiting A shoe box is shaped like a rectangular prism It is 39 4 centimeters long 17 8 centimeters wide and 11 4 centimeters tall Jacob. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

A shoe box is shaped like a rectangular prism. It is 39.4 centimeters long, 17.8 centimeters wide, and 11.4 centimeters tall. Jacob estimates that the surface area of the shoe box is about 2,800 square centimeters. Is his estimate reasonable?

Answer :

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KurtDavies KurtDavies · Answer 1 · 2024-09-23T12:57:12-04:00

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.