Flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if one m2 = 100 plants?

Correct answer:

V =  63.88 m3
n =  8100

Step-by-step explanation:

a=10 m b=9 m α=45  V=V1V2  u1=2 a=2 10=10 2 m14.1421 m u2=2 b=2 9=9 2 m12.7279 m   tan α =  u1/2  h1  tan α =  u2/2  h2  h1=u1/2 tanα=u1/2 tan45° =14.1421/2 tan45° =14.1421/2 1=7.07107 m h2=u2/2 tanα=u2/2 tan45° =12.7279/2 tan45° =12.7279/2 1=6.36396 m  V1=31 a2 h1=31 102 7.0711235.7023 m3 V2=31 b2 h2=31 92 6.364171.8269 m3  V=V1V2=235.7023171.8269=63.88 m3
n=b2 100=92 100=8100

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