Water reservoir

The cuboid reservoir contains 1900 hectoliters of water, and the water height is 2.7 m. Determine the bottom dimensions where one dimension is 2.2 m longer than the second.

Final Answer:

a =  7.36 m
b =  9.5605 m

Step-by-step explanation:

V=1900 hl→ m3=1900:10  m3=190 m3 c=2.7 m  V = abc S1​=V/c=190/2.7=271900​≐70.3704 m2 S1​ = ab b = 2.2+a  a(2.2+a)=S1​  a(2.2+a)=70.37037037037 a2+2.2a−70.37=0  p=1;q=2.2;r=−70.37 D=q2−4pr=2.22−4⋅1⋅(−70.37)=286.3214814815 D>0  a1,2​=2p−q±D​​=2−2.2±286.32​​ a1,2​=−1.1±8.460518 a1​=7.360518328 a2​=−9.560518328  a=a1​=7.3605=7.36 m

Our quadratic equation calculator calculates it.

b=a+2.2=7.3605+2.2≐9.5605 m   Verifying Solution:  V2​=a⋅ b⋅ c=7.3605⋅ 9.5605⋅ 2.7=190 m3

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