Question

The base of a solid is a region bounded by the curve (x^2/8^2)+(y^2/4^2)=1 (an ellipse with the major and minor axes of lengths 16 and 8 respectively). Find the volume of the solid if every cross section by a plane perpendicular to the major axis (x-axis) has the shape of an isosceles triangle with height equal to 1/4 the length of the base.

Answer 1

This is just like the other one The base of each triangle has length 2x,
making the area 1/2 bh = 1/2 (2x)(x/2) = 1/2 x^2
Using the symmetry of the figure,
v = 2∫[0,8] 1/2 x^2 dx

Answer 2

same oops as before.
v = 2∫[0,8] 1/2 y^2 dx = v = 2∫[0,8] 1/2 (16 - x^2/4) dx