Volume of the solid with given base, whose sections with the planes orthogonal to $y = 0$ are rectangles of height $4$

Question

Please help me to solve the following problem:

Determine the volume of the solid having as base the portion of cartesian plane limited by $y = 0$ and by $y = x^{3}$ in the closed interval $\left[-1,1\right]$, whose sections with the planes orthogonal to $y = 0$ are rectangles of height $4$.

Answer 1

$$\left(\int_0^1 x^3 dx\right)\cdot 2\cdot 4=2$$ We are able to double it since it's symmetrical to get rid of the "negative" since we're dealing with the shape rather than the value. This gives us the area of the base of the object, so we can multiply it by 4 and arrive at the answer