## anonymous 5 years ago Consider a solid whose base is a circle of radius r, and which has all cross-sections perpendicular to a particular diameter as equilateral triangles. Find an expression for A(x), the cross-sectional area of the slice. We did this question in class, so I have the answer, but we went through it really fast so I didn't get it. Now, doing it again, I'm not getting the right answer. What I did: A typical slice has sides 2√(r²-x²) A(x) = 1/2 * base * height base = 2√(r²-x²) height, I used sine rule and got 2√3 √(r²-x²) Which gives me A(x) = 2√3 (r² - x²) It should be √3 (r² - x²) Help please?

1. anonymous

what is x?

2. watchmath

The height should be $$\sqrt{3}\sqrt{r^2-x^2}$$. Remember you only use half of the base when you do the sine rule.