The axial section of the cone is a right-angled isosceles triangle, the leg of which is 16 cm.

The axial section of the cone is a right-angled isosceles triangle, the leg of which is 16 cm. Calculate the length of the height of the cone and the area of its base.

Since an isosceles triangle was obtained at the axial section, it means that both legs of this triangle are equal, which means if we denote the resulting triangle with letters ABC with the base BC, we get the following equality;

AB = AC = 16;

Since the triangle is rectangular, let’s use the Pythagorean theorem to find the base;

BC = √ (AB^2 + AC^2);

BC = √ (256 + 256);

BC = √512;

Since the hypotenuse of this triangle is equal to the diameter of the base of the cone, we find its area;

S = п* (√512) 2/4;

S = 3.14 * 512/4 = 401.92cm2;

Find the height using the formula, where R is the radius;

h = R = ВС / 2 = √512 * 2/2 = √ (256 * 2) * 2/2 = 16 * 2 * √2 / 2 = 32 * √2 / 2 = 16 * √2.