Thread: cross-sections help please

consider A, if A is the area bounded by y=x^2 and y=1. Suppose a solid has a base A nd the cros sections of the solid perpendicular to the yaxis are equilateral triangles. sketch solid nd find volume.

I know how to go about finding the area of A by evaluating the integral and I understand the concept of finding vol. by using cross sections but I dont know how to approach or start this problem. Can someone help please?

Hello, coe236!

is the area bounded by: .
Suppose a solid has a base A and the cross-sections of the solid
perpendicular to the y-axis are equilateral triangles.
Sketch solid and find volume.

The base looks like this:

Code:

                |
               1|
       *--------+--------*
                |
            x   |   x
        * - - - + - - - *
         *      |      *
           *    |    *
      - - - - - * - - - - - - 
                |

The area of an equilateral triangle with side is: .

The side of our equilateral triangle is: .

Hence, the area of the triangle is: .

Since , we have: .


Therefore, the volume is: .