<p>Would anyone be willing to explain/solve these problems for me? I'm really struggling with them for some reason and I don't even know where to begin. I think it's pretty obvious that I'm not mathematically inclined.</p>
<p>Find the volume of the solid with the given base and cross sections.</p>
<ol>
<li><p>The base is a unit circle x^2 + y^2 = 1 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.</p></li>
<li><p>The base is the region enclosed by y = x^2 and y = 3. The cross sections perpendicular to the y-axis are squares.</p></li>
</ol>
<p>3.The base is the region enclosed by y = x^2 and y = 3. The cross sections perpendicular to the y-axis are rectangles of height y^3.</p>
<p>Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.</p>
<ol>
<li>y = -x^2 + 4x - 3, y = 0, axis y = -1</li>
</ol>