The block

The block, the edges formed by three consecutive GP members, has a surface area of 112 cm2. The sum of the edges that pass through one vertex is 14 cm. Calculate the volume of this block.

Correct answer:

V =  64 cm3

Step-by-step explanation:

b= qa c = qa2 S=112 cm2  S = 2(ab+bc+ca) = 2(q a2 + q3a2 + q2a2) S = 2a2(q+q2+q3)  a+b+c=14 a+aq+aq2 = 14 a(1+q+q2)=14 a(q+q2+q3)=14q  S = 2a2(q+q2+q3) = 2a2 14q/a = 2 14 a q   b = aq b=2 14S=2 14112=4 cm  S = 2(b/q b + b q b + b q b/q)  S = 2(b2/q + b2 q + b2) S/2/b2 = 1/q+q+1  q S/2/b2=1+q2+q  q 112/2/42=1+q2+q q2+2.5q1=0 q22.5q+1=0  a=1;b=2.5;c=1 D=b24ac=2.52411=2.25 D>0  q1,2=2ab±D=22.5±2.25 q1,2=1.25±0.75 q1=2 q2=0.5 q=2  a=b/q=4/2=2 c=q b=2 4=8  V=a b c=2 4 8=64=64 cm3   Verifying Solution:  S1=2 (a b+b c+c a)=2 (2 4+4 8+8 2)=112 cm2 s1=a+b+c=2+4+8=14 cm

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