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