WAEC 2025 · Paper 1 · Q27✱✱

Solid mensuration

A cone is cut to leave a frustum with radii $12\text{ cm}$ and $6\text{ cm}$ and slant height $12\text{ cm}$ . Calculate the slant height of the full cone.

Worked solution (try it first)

Let the small cone cut off the top have slant height $s$ .
The full cone's slant height is $s + 12$ .
Similar cones: $\dfrac{s}{s + 12} = \dfrac{6}{12}$ , so $2s = s + 12$ and $s = 12$ .
The full cone's slant height is $12 + 12 = 24$ cm, option A.

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