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Nikitin
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Instead of the shell method, can't one find the volume of a sphere by integrating/summing its horizontal areas?
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Sure, if you mean using horizontal disks of thickness Δy. You can't sum areas to get a volume. You can sum increments of volume to get a total volume.Nikitin said:Instead of the shell method, can't one find the volume of a sphere by integrating/summing its horizontal areas?
The formula for calculating the volume of a sphere using circle areas is V = (4/3)πr^3, where V represents the volume and r represents the radius of the sphere.
The formula for the volume of a sphere is derived from the formula for the area of a circle, A = πr^2. By stacking multiple circles on top of each other with decreasing radii, we can create a sphere. The volume of each circle can be represented as A multiplied by the thickness of the sphere, which is equal to the radius. This results in the formula V = (4/3)πr^3.
No, the volume of a sphere cannot be directly calculated using the circumference of a circle. While the circumference is related to the radius, it does not contain enough information to determine the volume. The radius is needed to calculate the volume of a sphere.
Changing the radius of a sphere will have a direct impact on the volume. The volume of a sphere is directly proportional to the cube of the radius. This means that if the radius is doubled, the volume will increase by a factor of 8.
No, the volume of a sphere cannot be negative. Volume is a measure of the space occupied by an object, and it cannot be negative. Even if the radius of a sphere is negative, the volume will still be positive.