Cuboid and eq2

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

Correct result:

V =  18.2904 cm3

Solution:

h=6 cm S=48 cm2 S=4ah+2a2 48=46a+2a2  48=4 6 a+2 a2 2a224a+48=0 2a2+24a48=0  p=2;q=24;r=48 D=q24pr=24242(48)=960 D>0  a1,2=q±D2p=24±9604=24±8154 a1,2=6±7.7459666924148 a1=1.7459666924148 a2=13.745966692415   Factored form of the equation:  2(a1.7459666924148)(a+13.745966692415)=0  a=a1=1.7461.746  V=a2 h=1.7462 618.2904=18.2904 cm3   Verifying Solution:  S2=4 a h+2 a2=4 1.746 6+2 1.7462=48 cm2 S2=S

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