If the area of the axis section of a cone whose generatrix length is 4 is 8, the height of the cone is obtained

If the area of the axis section of a cone whose generatrix length is 4 is 8, the height of the cone is obtained

If the bus length is 4, the area of the axial section of the cone is 8, so s = 12ab · AC · sin ∠ BAC, 8 = 12 × 4 × 4 × sin ∠ BAC ﹥ sin ∠ BAC = 1, then ∠ DAC = 45 ° and ﹥ ad = abcos 45 ° = 22. The height of the cone is 22

If the generatrix length of the cone is 4 and the cross-section area passing through the axis is 8, then what is the height of the cone? (I don't know what the cross-section is.)

Then the area of the isosceles triangle with cross section is known, 8; the waist length is known, 4. Let the length of the bottom of the triangle (that is, the diameter of the bottom) be X. The isosceles triangle can be divided into two equal right triangles by the axis, the hypotenuse is the waist, and the length is 4; the bottom right side is the half diameter of the cone, From this we can list two equations: (a) area of isosceles triangle = 2 * area of right triangle = 2 * (x / 2 * h) / 2 = XH / 2 = 8 (b) Pythagorean theorem is used in right triangle, (x / 2) &# 178; + H & # 178; = 4 & # 178;
So we have the system of linear equations of two variables (a) XH = 16 (b) x & # 178 / 4 + H & # 178; = 16, and the solution H = 2 √ 2

If the generatrix of a cone is 8 and the apex angle of its axial section is right angle, then its side area is

The side view of the cone is an isosceles right triangle, the generatrix length r = 8, then the cone bottom radius r = 4, root sign 2
Bottom perimeter L = 2 * pi * r side perimeter L = 2 * pi * r
It is concluded that the ratio of the cone side area to the whole circle area is n = L / L = R / r = radical 2 / 2
Then the side area of the cone is s = n * pi * r square = 32 root sign 2 * PI

The generatrix length of a cone is 2. If the maximum cross-sectional area passing through its vertex is 2, the radius of the bottom of the cone can be calculated

The generatrix length of a cone is 2. If the maximum cross-sectional area passing through its vertex is 2,
When the maximum section area is 1 / 2 (2R) √ (2 & # 178; - R & # 178;) ≤ 2
r≥2