Multiple choice

The surface area of the frustum cone is given its base radius, R = 12 cm and top radius, r = 10 cm. The height of the cone is 12 cm. Find the slant height of the cone.

  1. $2\sqrt{37}$ cm
  2. $2\sqrt{5}$ cm

  3. 24 cm
  4. $3\sqrt{5}$ cm
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A Correct answer
Explanation

For a frustum, the slant height l = sqrt(h^2 + (R-r)^2). Here h=12, R=12, r=10. R-r = 2. l = sqrt(12^2 + 2^2) = sqrt(144 + 4) = sqrt(148) = sqrt(4 * 37) = 2 * sqrt(37).

AI explanation

The slant height of a frustum is found using the formula l = sqrt(h^2 + (R - r)^2). Plugging in the height of 12 cm and the radii of 12 cm and 10 cm gives l = sqrt(12^2 + (12 - 10)^2). This evaluates to sqrt(144 + 4), which simplifies to sqrt(148) or 2*sqrt(37) cm.

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