Digging a pit

The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m3 of soil were excavated when digging the pit?

Correct result:

V =  290.6667 m3

Solution:

a=14 m b=10 m α=13590=45  x=(ab)/2=(1410)/2=2 m tanα=x:h  h=x/tanα=x/tan45 =2/tan45 =2/1=2  S1=a2=142=196 m2 S2=b2=102=100 m2  S=S1+S1 S2+S2=196+196 100+100=436 m2  V=13 h S=13 2 436=8723=290.6667 m3



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