Quadrilateral 4S prism

The edge lengths of a quadrilateral prism are in the ratio a:b:c = 2:4:5. The surface of the prism is 57 cm2. Calculate the volume.

Final Answer:

V =  25.9808 cm3

Step-by-step explanation:

a: b:c = 2:4:5 S=57 cm2  a=2x b=4x c=5x  S = 2(ab+bc+ca) S/2 = 2x⋅ 4x + 4x⋅ 5x + 5x⋅ 2x S/2 = 8x2 + 20x2 + 10x2  x=2⋅ (8+20+10)S​​=2⋅ (8+20+10)57​​≐0.866 cm  a=2⋅ x=2⋅ 0.866=3​ cm≐1.7321 cm b=4⋅ x=4⋅ 0.866=2 3​ cm≐3.4641 cm c=5⋅ x=5⋅ 0.866≐4.3301 cm  V=a⋅ b⋅ c=1.7321⋅ 3.4641⋅ 4.3301=15 3​≐25.9808 cm3   Verifying Solution:   S1​=2⋅ (a⋅ b+b⋅ c+c⋅ a)=2⋅ (1.7321⋅ 3.4641+3.4641⋅ 4.3301+4.3301⋅ 1.7321)=57 cm2

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You need to know the following knowledge to solve this word math problem:

algebraarithmeticsolid geometryplanimetricsbasic operations and conceptsUnits of physical quantitiesGrade of the word problem

 
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