17 июн. 2014 г. · A derivative is a rate of change. When a sphere increases in size, what happens? It expands outward, adding more mass to the surface. When you ... |
13 сент. 2017 г. · If an n-sphere's "volume" can be defined by a function V, then its first derivative is its "surface area", that is, the boundary of its "volume". |
15 мар. 2019 г. · The derivative is a rate of change. In this case, the derivative of the volume with respect to its radius is the surface area. What this means, ... |
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24 февр. 2016 г. · The volume of any hypersphere (n-dimensional version of a sphere) is Vn(r) and its derivative is the surface area of the hypersphere An(r). |
30 нояб. 2017 г. · [Mathematics] The derivative of the volume of a sphere is the surface area. The derivative of the surface area is 8pi*r. What does this term ... |
9 февр. 2021 г. · So, the volume of a sphere increases by a shell of a certain thickness as you increase the radius. Now, notice that a cylinder also has this ... |
29 февр. 2016 г. · The derivative of a function is the rate of change in that function. Imagine we have a volume V(t) and we let t vary from t0 to t0 + h. We can ... |
18 мая 2014 г. · Yes. If S(r) is the surface area of a sphere of radius r, and dr is an infinitesimal change in the radius, then S(r) ... |
8 июл. 2024 г. · The surface of a sphere is the derivative of it's volume. Is this a direct corollary of the Stokes theorem? |
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