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Interactive video lesson plan for: Volume of a Sphere

Activity overview:

You will learn about "Volume of a Sphere" in this video. Sphere is a perfectly round three-dimensional object. Let us find the formula to find the volume of a sphere.

For this, let us divide the sphere into equal sized pyramids with same base and height. We know that, Volume of a pyramid = 1/3 Area of base x Height. As the vertex of each pyramid coincides with the centre of sphere, the height of each pyramid is equal to the radius of the sphere. Thus, volume of each of these pyramids is 1/3Ar, where A is area of the base. Now, volume of the sphere is the total volume of all these pyramids. So, if the volume of the 1st pyramid is 1/3A1r, volume of the second pyramid is 1/3A2r, the volume of the last pyramid will be, say, 1/3Anr. Therefore, Volume of sphere = 1/3 r (A1 + A2... + An).

An important point is that base area of all pyramids together makes the surface area of sphere, i.e. 4 pi r2. Therefore (A1, A2... An) = 4 pi r2. Therefore Volume of sphere = 1/3 r * (4 pi r2) = 4/3 pi r3

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