# Volume of Described Solid

Nicolaus

## Homework Statement

The base of S is the triangular region with vertices (0, 0), (5, 0), and (0, 5). Cross-sections perpendicular to the y-axis are equilateral triangles.
Find V of described triangle.

## The Attempt at a Solution

I first wrote the equation of the line in terms of x (x = 4-y), which is the base. Since we are dealing with an equilateral triangle the area of the cross section would be A(y)= ((4-y)^2)/2 and so the integral to calculate the volume is A(y)dy from 0 to 4.
Since I am arriving at the supposedly wrong answer, what am I missing?

Mentor

## Homework Statement

The base of S is the triangular region with vertices (0, 0), (5, 0), and (0, 5). Cross-sections perpendicular to the y-axis are equilateral triangles.
Find V of described triangle.

## The Attempt at a Solution

I first wrote the equation of the line in terms of x (x = 4-y), which is the base.
I don't see where your equation comes from. What's the equation of the line between (5, 0) and (0, 5)?
Since we are dealing with an equilateral triangle the area of the cross section would be A(y)= ((4-y)^2)/2 and so the integral to calculate the volume is A(y)dy from 0 to 4.
Since I am arriving at the supposedly wrong answer, what am I missing?

• 1 person
Nicolaus
It's a typo; meant 5-y. I figured out the problem. Thanks for your interest in helping.