Volume of a Solid with Square Cross Sections
A solid has square cross sections perpendicular to the y-axis. The side length of a cross section at height $$y$$ is given by $$s(y)=y+1$$. All of the following statements about the volume of the solid are true EXCEPT:
A
The volume is obtained by integrating the perimeter of the square, i.e., $$V=\int_{a}^{b} 4*(y+1) dy$$, over the interval.
B
Each square cross-sectional area is given by $$(y+1)^2$$.
C
The volume is computed as $$V=\int_{a}^{b} (y+1)^2 dy$$ by summing the areas of the cross sections.
D
Using the area formula for squares in conjunction with integration yields the total volume of the solid.
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