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1 min read•june 8, 2020

Anusha Tekumulla

This topic is very similar to topic 8.7 except now we’re **using triangles and semicircles as cross sections**. To find the **area of a shape using a triangle or semicircle cross section**, take a look at the example below.

Let’s say we are asked to find the volume of a solid whose base is the circle x^2 + y^2 = 4, where the cross sections perpendicular to the x-axis are all equilateral triangles. NOTE: Sometimes you'll be given isosceles right triangles or semicircles. Make sure you using the right formula!

We find the side of the triangle by doing **top minus bottom**. Thus, the side of the triangle is 2√4 - x^2. Now, we **use the formula for the equilateral triangle to find the area of the cross section** (A = (side)2 * √3 / 4). We can now find the volume by **integrating the area function** from x = -2 to x = 2.

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