Question

The base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x^2. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid?

Answer 1

whats the formula for the area of an equi tri?

Answer 2

for some side length k

k sin(60) = height
k is the base

k^2 sin(60)/2 seems approapriate

in this case, k is the distance between y=x and y=x^2

Answer 3

also, the dimensions are meaningless since we simply dont know what scale the xy grid uses to start with.