Consecutive 46761

The block lengths are made up of three consecutive GP members. The sum of the lengths of all edges is 84 cm, and the volume
block is 64 cm3. Determine the surface of the block.

Correct answer:

S =  672 cm2

Step-by-step explanation:

a+b+c=84 cm V=64 cm3  b=q a c=q2 a  V =abc = a3 q3 = (a q)3 = b3  b=3V=364=4 cm  a+c=84b ac = V/b a(84ba) = V/b  a(84ba)=V/b  a(844a)=64/4 a2+80a16=0 a280a+16=0  p=1;q=80;r=16 D=q24pr=8024116=6336 D>0  a1,2=2pq±D=280±6336=280±2411 a1,2=40±39.799497 a1=79.799497484 a2=0.200502516  a=a2=0.20050.2005 c=V/(b a)=64/(4 0.2005)79.7995 cm  S=2 (a b+b c+a c)=2 (0.2005 4+4 79.7995+0.2005 79.7995)=672=672 cm2   Verifying Solution:  V2=a b c=0.2005 4 79.7995=64 cm3 s2=a+b+c=0.2005+4+79.7995=84 cm q1=b/a=4/0.200519.9499 q2=c/b=79.7995/419.9499

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