The radius of the base of the cone is 1. The axial section is an equilateral triangle. Find the area of the axial section.

The axial section of a cone is a plane passing through its axis. Since the cone is formed by the rotation of the triangle, the triangle also acts as an axial section. This section is an equilateral triangle, that is, a triangle in which all sides are equal and amount to 1 cm.

To calculate its area, it is most convenient to apply Heron’s formula:

S = √p (p – a) (p – b) (p – c); Where:

S is the area of ​​the triangle;

p – semi-perimeter (p = P / 2);

a, b, c – sides of the triangle;

p = (1 + 1 + 1) / 2 = 3/2 = 1.5;

S = √1.5 * (1.5 – 1) * (1.5 – 1) * (1.5 – 1) = √1.5 * 0.5 * 0.5 * 0.5 = √0 , 1875 ≈ 0.43 cm2.

Answer: the area of ​​the axial section of the cone is 0.43 cm2.