Answer:
V = 18x^3 +48x^2 +(32 -8π)x cubic inchesStep-by-step explanation:
The volume of soil in the frame can be found by finding the volume of the rectangular prism created by the frame subtracting the volume of the pots.
The frame contains 4 pots of diameter 2 inches, so their total area is ...
A = 4(πr^2) = 4(π(1 in)^2) = 4π in^2
The dimensions of the frame, in inches are ...
length: (3x +4) inches
width: (3x +4) inches
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: 2x inches
So the volume of soil in the frame is ...
V = (LW - 4π)(2x)
V = ((3x +4)(3x +4) -4π)(2x) = (2x)(9x^2 +24x +16 -4π)
V = 18x^3 +48x^2 +(32 -8π)x cubic inches