The generatrix of the cone is 34 and is inclined to the base plane at an angle of 60 degrees.
| April 20, 2021 | education
The generatrix of the cone is 34 and is inclined to the base plane at an angle of 60 degrees. Find the area of the lateral surface of the cone.
The top of the cone, point B is projected to point O, the center of the circle.
Triangle AOB is rectangular. The sum of the acute angles of a right-angled triangle is 90, then the angle ABO = (90 – 60) = 30.
The leg AO = R and lies opposite the angle 30, then its length is equal to half the length of the hypotenuse AB.
R = AB / 2 = 34/2 = 17 cm.
Let us determine the area of the lateral surface of the cone.
Sside = π * R * L = π * 17 * 34 = 578 * π cm2.
Answer: The lateral surface area is 578 * π cm2.
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