Cuboid and eq2

Calculate the volume of a cuboid with a square base and height of 6 cm if the surface area is 48 cm2.

Correct answer:

V =  18.2904 cm3

Step-by-step explanation:

h=6 cm S=48 cm2 S = 4ah +2a2 48=4 6 a+2 a2  48=4 6 a+2 a2 2a224a+48=0 2a2+24a48=0 2 ...  prime number 24=233 48=243 GCD(2,24,48)=2  a2+12a24=0  p=1;q=12;r=24 D=q24pr=12241(24)=240 D>0  a1,2=2pq±D=212±240=212±415 a1,2=6±7.745967 a1=1.745966692 a2=13.745966692  a=a1=1.7461.746  V=a2 h=1.7462 618.2904 cm3   Verifying Solution:  S2=4 a h+2 a2=4 1.746 6+2 1.7462=48 cm2 S2=S

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