The plaster cast

The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area.

Correct answer:

V =  29.4628 m3
S =  68.3013 m2

Step-by-step explanation:

a=5 m S1=a2=52=25 m2  a2=(a/2)2+h12  h1=a2(a/2)2=52(5/2)24.3301 m  h12=h22+(a/2)2  h2=h12(a/2)2=4.33012(5/2)23.5355 m  V=13 S1 h2=13 25 3.5355=29.4628 m3
S2=12 a h1=12 5 4.330110.8253 m2  S=4 S2+S1=4 10.8253+25=68.3013 m2



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