Posted by admin | Posted in Outdoor Cooking | Posted on 25-12-2007
Tags: diy, hardware, plastic, retro, yellow, yellow plastic chain, yellow plastic gas line, yellow plastic gas pipe, yellow plastic island coat, yellow plastic plates
Another question of mathematics. How I can use integration to find the volume of a yellow plastic ball.?
This ball 3.0 inches tall. The circumference is 10.0 inches. Therefore, the radius is 5 inches. I know that V = (pi) r squared) (height). My question is how integrating this formula?
The radius is half the diameter, half the circumference, so that the radius is 1.5 ". The easiest way to do it is a triple integral using spherical coordinates. I derive the general equation for the volume of a sphere, and then we can connect the radius of 1.5 "to find the specific outcome. In 3-D spherical coordinates, integrating using a sphere and double the result to avoid the cancellation of the sinusoidal rotation itself Full … 2 S [θ = 0:180 °] S [φ =- 90:90 °] S [r = 0:] R ² r sinθ dφ dθ dr 2 S [θ = 0:180 °] S [90:90 φ =- °] (R ³ / 3) sinθ dθ dφ 2 S [θ = 0:180 °] (R ³ / 3) (π / 2 + π / 2) sinθ dθ 2πR ³ / 3 [-cos (180 °) + cos (0 °)] 2πR ³ / 3 (1 + 1) 4πR ³ / 3 Replace R with 1.5 "and multiply by yellow, and you get … 4π (1.5) ³ / 3 = 14,137 in ³ / / notation: since there is no good way to kind integral notation, I am using this format simple enough: S [x = a: b] x dx which read "the integral of x dx as x goes from A to B".
yellow plastic cap (2yrs later)
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