Volume of the Sphere
Date: Fri, 4 Nov 94 21:06 NZDT From: Joy Subject: WHAT IS THE VOL. OF A SPHERE Dear Dr. Maths I am an eighth grader. I am having difficulty with maths. Could you please tell me what the volume of a sphere is. How can I calculate it. Thank you.
Date: Fri, 4 Nov 1994 08:13:05 +0900 Hi Joy- Thanks for writing. The volume of a sphere can be calculated as long as you know the radius of the sphere - call it r. Then the volume is (4/3)*pi*r^3. That is four thirds times pi times r cubed. Have you worked on volumes of other solids yet? In general the volume of any cone or pyramid (a 3-d solid that has a two-d base, like a square, triangle, or circle and a point not on the plane that the base figure is connected to, like the Egyptian Pyramids or an ice cream cone) is the area of the base times 1/3 of the height. As it turns out this is related to the volume of a sphere. Consider the cone whose base is the same size as the circumference of the sphere at its largest point and with height equal to the radius of the sphere. In other words, this cone would "fit inside" of the semi-sphere. From the formula I mentioned above, the volume of the cone is (1/3)*r*area of the base. The area of the base is the area of a circle with radius r: pi*r^2. So the volume is (1/3)pi*r^3. This is exactly half of the volume of the semi-sphere. If you add them together, you get (3/3)pi*r^3 = pi*r^3, which is the volume of a cylinder with radius r and height r. Can you picture this? What do you think? Please write back if you have more questions about this or some other topic. -Margaret, MD on call.
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