Question
transform y=(x-2)^3 into a volume equation based off of v(r)=4/3pier^3
Answers
GPT 3.5
To transform the equation y = (x - 2)^3 into a volume equation based on V(r) = (4/3)πr^3, we need to establish a relationship between x and r.
We know that the volume equation V(r) represents the volume of a sphere with radius r. To relate it to the given equation, we need to find a connection between the x-coordinate in the equation y = (x - 2)^3 and the radius r in the volume equation.
We can set x - 2 = r, which implies that x = r + 2.
Substituting this in the equation y = (x - 2)^3, we have:
y = (r + 2 - 2)^3
y = r^3
Now, we have the volume equation in terms of y: V(r) = (4/3)πy.
So, the transformed volume equation based on V(r) = (4/3)πr^3 for the equation y = (x - 2)^3 is:
V(r) = (4/3)πr^3.
We know that the volume equation V(r) represents the volume of a sphere with radius r. To relate it to the given equation, we need to find a connection between the x-coordinate in the equation y = (x - 2)^3 and the radius r in the volume equation.
We can set x - 2 = r, which implies that x = r + 2.
Substituting this in the equation y = (x - 2)^3, we have:
y = (r + 2 - 2)^3
y = r^3
Now, we have the volume equation in terms of y: V(r) = (4/3)πy.
So, the transformed volume equation based on V(r) = (4/3)πr^3 for the equation y = (x - 2)^3 is:
V(r) = (4/3)πr^3.