Final answer:
To minimize the amount of material needed to construct a pyramid, you need to consider the surface area. Based on the calculations, option b) with b = 8.5 in. and s = 3.5 in. would minimize the amount of material needed.
Step-by-step explanation:
In order to minimize the amount of material needed to construct a pyramid, we need to consider the surface area of the pyramid. The surface area is directly related to the dimensions of the pyramid. The formula for the surface area of a pyramid is:
Surface Area = base area + (0.5 * perimeter * slant height)
By comparing the given dimensions, we can calculate the surface area for each option:
- a) Surface Area = (7.56 * 7.56) + (0.5 * (4 * 7.56) * 3.8) = 57.408 + 57.408 = 114.816
- b) Surface Area = (8.5 * 8.5) + (0.5 * (4 * 8.5) * 3.5) = 72.25 + 59.5 = 131.75
- c) Surface Area = (6 * 6) + (0.5 * (4 * 6) * 6) = 36 + 72 = 108
- d) Surface Area = (3.8 * 3.8) + (0.5 * (4 * 3.8) * 7.56) = 14.44 + 57.408 = 71.848
Based on the calculations, option b) b = 8.5 in. and s = 3.5 in. would minimize the amount of material needed to construct the pyramid.