The volume of the cone is 16π cm³, and its height is 3 cm long, find the side surface of the cone.
| June 10, 2021 | education
From the formula for the volume of the cone, we express the radius of the circle at its base.
V = Sosn * h / 3 = π * R ^ 2 * OB / 3.
R ^ 2 = 3 * V / π * OB = 3 * 16 * π / π * 3 = 16 cm2.
R = AO = 4 cm.
In a right-angled triangle AOB, by the Pythagorean theorem, we determine the length of the generator of the cone AB.
AB ^ 2 = AO ^ 2 + OB ^ 2 = 16 + 9 = 25.
AB = 5 cm.
Let us determine the area of the lateral surface of the cone.
Side = π * R * L = π * AO * AB = π * 4 * 5 = 20 * π cm2.
Answer: The lateral surface area is 20 * π cm2.
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