To find the scale factor of the cones, we can use the formula for volume of a cone: V = (1/3)Ï€r^2h.
Let's denote the scale factor as k. We can set up the following equation:
V(R) = k^3 * V(S)
Given that V(R) = 1331 cubic feet and V(S) = 64 cubic feet, we can substitute these values into the equation:
1331 = k^3 * 64
To solve for k, divide both sides of the equation by 64:
1331 / 64 = k^3
Taking the cube root of both sides gives us:
∛(1331 / 64) = k
Simplifying the expression:
∛(1331 / 64) = ∛(1331) / ∛(64) = 11 / 4
Therefore, the scale factor of Cone R to Cone S is 11/4.