- #1
The formula for finding the volume of a sphere in spherical coordinates is V = (4/3) * π * r^3, where r is the radius of the sphere.
To convert from Cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ), use the following formulas:
r = √(x^2 + y^2 + z^2)
θ = arccos(z/r)
φ = arctan(y/x)
Yes, you can use spherical coordinates to find the volume of a hemisphere. The formula for the volume of a hemisphere is V = (2/3) * π * r^3. Simply plug in the radius of the hemisphere into the formula.
As the radius of a sphere increases, the volume also increases. This is because the volume of a sphere is directly proportional to the cube of its radius.
Yes, the formula for finding the volume of a sphere in spherical coordinates can be used regardless of the units used for the radius. Just make sure that the units for the radius are consistent with the units used for π (e.g. if the radius is in meters, π should also be in meters).
