Cuboid and eq2

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

Result

V =  1133.71 cm3

Solution:

h=6 S=48 S=4ah+2a2  48=4⋅ 6⋅ a+2a2 −2a2−24a+48=0 2a2+24a−48=0  p=2;q=24;r=−48 D=q2−4pr=242−4⋅2⋅(−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(a−1.7459666924148)(a+13.745966692415)=0a=a2=(−13.746)≐−13.746 S2=4a⋅ h+2a2=4⋅ (−13.746)⋅ 6+2⋅ (−13.746)2=48 V=a2⋅ h=(−13.746)2⋅ 6≐1133.7096=1133.71 cm3h = 6 \ \\ S = 48 \ \\ S = 4ah +2a^2 \ \\ \ \\ 48 = 4 \cdot \ 6 \cdot \ a+2a^2 \ \\ -2a^2 -24a +48 = 0 \ \\ 2a^2 +24a -48 = 0 \ \\ \ \\ p = 2; q = 24; r = -48 \ \\ D = q^2 - 4pr = 24^2 - 4\cdot 2 \cdot (-48) = 960 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ -24 \pm \sqrt{ 960 } }{ 4 } = \dfrac{ -24 \pm 8 \sqrt{ 15 } }{ 4 } \ \\ a_{1,2} = -6 \pm 7.7459666924148 \ \\ a_{1} = 1.7459666924148 \ \\ a_{2} = -13.745966692415 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (a -1.7459666924148) (a +13.745966692415) = 0a = a_{ 2 } = (-13.746) \doteq -13.746 \ \\ S_{ 2 } = 4a \cdot \ h +2a^2 = 4 \cdot \ (-13.746) \cdot \ 6 +2 \cdot \ (-13.746)^2 = 48 \ \\ V = a^2 \cdot \ h = (-13.746)^2 \cdot \ 6 \doteq 1133.7096 = 1133.71 \ cm^3

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