Find the Volume of Spheres using Integral Calculus

Hi friends! This video is about deriving and finding the volume of a sphere by using integral calculus!

The formula for the volume of any shape is the definite integral from one end of the shape (let's call it "a") to the other end of the shape (let's call this "b"). So the integral is from a to b of the area of the cross-section (If you cut or slice the shape, you find the area of the open surface) and then dx.

Here, the area of the cross-section of the sphere is the circle! The area of a circle is pi times the radius squared. From the figure shown, the radius is y. Using the Pythagorean theorem, we get y = (r^2-x^2)^0.5. Plugging this into the area of the circle, we get A = pi(r^2-x^2). Now, we substitute this into the integral from -r to r and solve for it. Done.

In the next video, I will show you how to find the volume of a cone using integration.

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