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To find the radius of the cone, we need to rearrange the volume formula to solve for the radius.
V = 13πr^2h
500 = 13πr^2(13.5)
500 = 13π(182.25)r^2
r^2 = 500 / (13 * π * 182.25)
r^2 ≈ 0.0919
r ≈ √0.0919
r ≈ 0.303 cm
Therefore, the approximate radius of the cone is 0.303 cm.