The area of the base of the cone is 16, and the area of the lateral surface is 24. Find the generator of the cone.
| April 4, 2021 | education
The lateral surface area of the cone can be determined by the formula
Sside = n * R * L,
where R is the radius of the base of the cone, L is the length of its generatrix.
Then the required length of the generator is
L = S side / (n * R).
The base of the cone is a circle, so its area can be calculated using the formula
Sosn = n * R ^ 2,
whence the radius of the base is
R = √ (Sb / p).
Then the length of the generator will be equal to
L = S side / (p * √ (S main / p)) = S side / √ (p * S main);
L = 24 / √ (3.14 * 16) = 3.4.
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