Regular square prism

The volume of a regular square prism is 192 cm3. The size of its base edge and the body height is 1:3. Calculate the surface of the prism.

Correct answer:

S =  218.9202 cm2

Step-by-step explanation:

V=192 cm3 a:d=1:3 d = 3a  V = a2 h s = 2  a h2 = d2 s2 = d2 2a2 = 9a2 2a2 h2 = 7a2 h = 7 a  V = a2 h V = a2 7 a V = a3 7  a=3V/7=3192/74.1711 cm  h=7 a=7 4.171111.0357 cm  S=2 a2+4 a h=2 4.17112+4 4.1711 11.0357218.9202 cm2   Verifying Solution:  V2=a2 h=4.17112 11.0357=192 cm3 d2=h2+a2+a2=11.03572+4.17112+4.1711212.5133 cm k2=d2/a=12.5133/4.1711=3

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