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Answer:
V = 36x^3 +102x^2 +(72 -18π)x cubic inches
Step-by-step explanation:
The frame contains 6 pots of diameter 2 inches, so their total area is ...
A = 6(πr^2) = 6(π(1 in)^2) = 6π in^2
The dimensions of the frame, in inches are ...
length: 4x +6
width: 3x +4
The area of the pots will subtract from the area of the frame to give the area covered by soil. The other dimension of the frame is ...
height: 3x
So the volume of soil in the frame is ...
V = (LW - 6π)(3x)
V = ((4x +6)(3x +4) -6π)(3x) = 3x(12x^2 +34x +24 -6π)
V = 36x^3 +102x^2 +(72 -18π)x . . . . cubic inches