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The problem of finding the area of conical surface in high school mathematics
Solution: If the diameter of cone bottom circle is 6, the radius of cone bottom circle r=3, and the length of bus L is 5.

The radius r, length l and height h of the cone base circle form a right triangle.

Is the height h=4 calculated by Pythagorean theorem? .

The surface area of the cone is equal to the area of the side surface plus the area of the bottom circle.

∫ lateral area of the cone = π times the radius of the bottom circle of the cone times the generatrix = π× 3× 5 =15 π;

The area of the bottom circle of the cone =π×3? =9π;

The surface area of the cone = 15π+9π=24π.

draw

Another solution: the side of the cone is a sector, the radius of the sector is the generatrix length L of the cone, and the arc length of the sector is the circumference of the bottom circle of the cone c=2πr=6π. The central angle θ = C/L = 6π/5 = 2 16.

∫S fan = 2 16/360 *π* l * l = 15π

S bottom =π*r? =9π

∴S table =24π≈24*3. 14=75.36