Calculate the lateral surface area of a cone if its axial cross-sectional area is 12cm² and the base area is 16π cm².
| July 18, 2021 | education
Knowing the area of the base, we determine the radius of the circle at the base of the cone.
Sosn = n * R ^ 2.
16 * n = n * R ^ 2.
R ^ 2 = 16.
R = 4 cm.
The axial section of the cone is an equilateral triangle, in which the sides AC and BC are equal and are the generatrix of the cone.
Ssech = AO * CO = R * CO.
12 = 4 * CO.
CO = 3 cm.
In a right-angled triangle ACO, we define the hypotenuse AC.
AC ^ 2 = R ^ 2 + CO ^ 2 = 16 + 9 = 25.
AC = 5 cm.
Let us determine the area of the lateral surface of the prism.
S side = n * R * AC = n * 4 * 5 = 20 * n.
Answer: The area of the lateral surface of the prism is 20 * n cm2.
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