Multiple choice

If slant height of a cone is $13$ cm and the base radius is $5$ cm, then the height of cone is :

  1. $12cm$
  2. $8cm$
  3. $10cm$
  4. $18cm$
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A Correct answer
Explanation

In a right-angled triangle formed by the height, radius, and slant height of a cone, h^2 + r^2 = l^2. h^2 + 5^2 = 13^2 => h^2 + 25 = 169 => h^2 = 144 => h = 12.

AI explanation

The relationship between the height, radius, and slant height of a cone is given by the Pythagorean identity: l^2 = r^2 + h^2. Substituting the given values results in 13^2 = 5^2 + h^2, which simplifies to 169 = 25 + h^2. Solving for h gives h^2 = 144, meaning the height is 12 cm.

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