The generatrix in the cone is 5, the height is 4. Find the volume of the cone.
| January 28, 2021 | education
The vertex B of the cone is projected to point O, the center of the circle.
Triangle AOB is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg OA.
ОА ^ 2 = R ^ 2 = AB ^ 2 – ОВ ^ 2 = 25 – 16 = 9.
OA = 3 cm.
Determine the area of the circle at the base of the cone.
S main = π * R ^ 2 = 9 * π cm2.
Let’s define the volume of the cone.
V = Sosn * ОВ / 3 = 9 * π * 4/3 = 12 * π cm3.
Answer: The volume of the cone is 12 * π cm3.
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