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?

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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?

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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what is x?
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.

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