The radius of the base of the cone is 20 cm. The distance from the center of the base
| February 10, 2021 | education
The radius of the base of the cone is 20 cm. The distance from the center of the base to the generatrix is 12 cm. Find the area of the lateral surface of the cone.
Since OH is the distance from point O to the generatrix AB, then OH is perpendicular to AB.
In a right-angled triangle AOН, according to the Pythagorean theorem, we determine the length of the leg AН.
AH ^ 2 = AO ^ 2 – OH ^ 2 = 400 – 144 = 256.
AH = 16 cm.
OH is the height of a right-angled triangle, drawn to the hypotenuse, then the AOB triangle is similar to the AOН triangle.
AB / AO = AO / AН.
AB = AO * AO / AH = 400/16 = 25 cm.
Let us determine the area of the lateral surface of the cone.
Side = π * AO * AB = π * 20 * 25 = 500 * π cm2.
Answer: The lateral surface area is 500 * π cm2.
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