The volume of a pyramid varies jointly as the height and the area of the base. If a pyramid has the measurements V=1144cubic meters, l=8 meters and w=11 meters, and h=39 meters, what is the volume of a pyramid that has a length of 15 meters, width of 46 meters, and height of 48 meters. Round your answer to the nearest hundredth.Find the value of k ( rounded to the nearest hundredth ). Using the value of k, find an equation that represents the general relationship indicated above
Accepted Solution
A:
Answer:11040 m³k ≈ 0.33V = (1/3)BhStep-by-step explanation:The given relation is ... V = kBh . . . . . for some base area B, height h, and constant of variation kWe are given length and width of the base so we presume it is a rectangle. B = l·w = 8·11 = 88 . . . . square metersThe given volume tells us the value of k: 1144 = k(88)(39) . . . . . . cubic meters 1144/3432 = k = 1/3 ≈ 0.33The value of k is about 0.33.__Then the volume of the larger pyramid is ... V = (1/3)(15 m)(46 m)(48 m) = 11,040 m³The general relationship is ... V = 1/3Bh