The curved surface area of the frustum cone shaped bucket is $360 \pi \space\ cm^2$. The top and bottom diameter of the bucket is $6$cm and $12$ cm. What is the slant height?

Using the curved surface area formula for a frustum of a cone, the area equals pi multiplied by the sum of the top and bottom radii and the slant height. The radii are half of the given diameters, making them 3 cm and 6 cm. Substituting the values gives 360 pi equals pi multiplied by the sum of 3 and 6 and the slant height, which simplifies to 40 equals the slant height. The slant height is 40 cm.

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