The regular

The regular quadrilateral pyramid has a volume of 24 dm3 and a height of 45 cm. Calculate its surface.

Correct result:

S =  55.3954 dm2

Solution:

V=24 dm3 v=45 cm→ dm=45/10  dm=4.5 dm  V=13⋅ S1⋅ v  S1=3⋅ V/v=3⋅ 24/4.5=16 dm2  a=S1=16=4 dm  h2=v2+(a/2)2=4.52+(4/2)2≐4.9244 dm  S2=a⋅ h22=4⋅ 4.92442=97 dm2≐9.8489 dm2  S=S1+4⋅ S2=16+4⋅ 9.8489=55.3954 dm2

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