Cuboid

A cuboid with edge a = 6 cm and space diagonal u = 31 cm has a volume of V = 900 cm³. Calculate the lengths of the other two edges.

Final Answer:

b =  30 cm
c =  5 cm

Step-by-step explanation:

a=6 cm V=900 cm3 u=31 cm  V = abc 900 = 6 bc bc = 150  u =  a2+b2+c2 ​  312 = 62 + b2 + c2  925 = b2 + c2 925 =  c2 22500​ + c2  c4−925 c2 + 22500 = 0 x = c2  x2−925x+22500=0  x2−925x+22500=0  a=1;b=−925;c=22500 D=b2−4ac=9252−4⋅1⋅22500=765625 D>0  x1,2​=2a−b±D​​=2925±765625​​ x1,2​=2925±875​ x1,2​=462.5±437.5 x1​=900 x2​=25  c1​=x1​​=900​=30 c2​=x2​​=25​=5  b=c1​=30=30 cm

Our quadratic equation calculator calculates it.

c=c2​=5=5 cm   Verifying Solution:  d=a2+b2+c2​=62+302+52​=31 d=u V2​=a⋅ b⋅ c=6⋅ 30⋅ 5=900 cm3 V2​ = V

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

algebraarithmeticsolid geometryplanimetricsUnits of physical quantitiesGrade of the word problem

 
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