The base area of the cone is 16, the angle between the generatrix and the base plane is 60 degrees
| March 4, 2021 | education
The base area of the cone is 16, the angle between the generatrix and the base plane is 60 degrees, find the total surface area.
Knowing the area of the base of the cone, we determine its radius.
Sb = π * R ^ 2 = π * AO ^ 2 = 16 * π cm2.
AO ^ 2 = 16.
AO = 4 cm.
The ABO triangle is rectangular, in which the angle ABO = (90 – ОАВ) = (90 – 60) = 30.
The AO leg lies opposite an angle of 300, then its length is equal to half the length of the hypotenuse AB.
AO = AB / 2.
AB = 2 * AO = 2 * 4 = 8 cm.
Then the lateral surface area is equal to: Side = π * R * L = π * AO * AB = π * 4 * 8 = 32 * π cm2.
Sпов = Sсн + Sside = 16 * π + 32 * π = 48 * π cm2.
Answer: The total surface area of the cone is 48 * π cm2.
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