To clarify, it seems you're asking for the radius of the base of the cone rather than a "length," as the dimensions you've provided refer to a cone's height, slant height, and base diameter rather than length.
However, the base "length" you've mentioned as 2 might be a bit confusing. Typically, we refer to the base of a cone by its radius (r) or diameter (d). If we assume that the base length refers to the diameter (d), then the radius would be half of that:
\[ r = \frac{d}{2} = \frac{2}{2} = 1 \]
Now, we can check the validity of the given heights. We can use the Pythagorean theorem as a relationship between the height \(h\), radius \(r\), and slant height \(s\):
\[ s^2 = r^2 + h^2 \]
Plugging in the values:
\[ 4^2 = 1^2 + 6^2 \]
Calculating the squares:
\[ 16 = 1 + 36 \]
\[ 16 = 37 \]
This does not hold true. It appears that there’s a mistake in the dimensions provided because the height cannot simultaneously be 6 and have a slant height of 4 with a base diameter of 2.
Since the calculated values do not provide a correct geometric relationship, please verify the dimensions you provided for the cone.
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