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 −2a2−24a+48=0 2a2+24a−48=0 2 ...  prime number 24=23⋅3 48=24⋅3 GCD(2,24,48)=2  a2+12a−24=0  p=1;q=12;r=−24 D=q2−4pr=122−4⋅1⋅(−24)=240 D>0  a1,2​=2p−q±D​​=2−12±240​​=2−12±415​​ a1,2​=−6±7.745967 a1​=1.745966692 a2​=−13.745966692  a=a1​=1.746≐1.746  V=a2⋅ h=1.7462⋅ 6≐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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