Centimeters - block

The surface of the block is 4596 square centimeters. Its sides are in a ratio of 2:5:4. Calculate the volume of this block.

Correct answer:

V =  18810.9025 cm3

Step-by-step explanation:

S=4596 cm2 S = 2(ab+bc+ca) a:b:c=2:5:4 = 2k:5k:4k  S = 2 (2k 5k + 5k 4k + 4k 2k)  k=S/2/(2 5+2 4+5 4)=4596/2/(2 5+2 4+5 4)7.7765 cm  a=2 k=2 7.776515.553 cm b=5 k=5 7.776538.8824 cm c=4 k=4 7.776531.1059 cm  V=a b c=15.553 38.8824 31.105918810.9025 cm3   Verifying Solution:   S2=2 (a b+b c+c a)=2 (15.553 38.8824+38.8824 31.1059+31.1059 15.553)=4596 cm2



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