Conical surface area formula

Conical surface area formula

Surface area of cone = side area of cone + area of bottom circle
Where: side area of cone = π RL
The total area of the cone = π RL + π R2
R is the radius of the circle at the bottom of the cone
L is the generatrix length of the cone

Formula of sector area formula of cone area formula of cone platform area

Sector is an important figure related to circle. Its area is related to center angle (vertex angle) and circle radius. The area of sector with center angle of n ° and radius of R is n / 360 * π R ^ 2. If the vertex angle is in radian unit, it can be simplified as 1 / 2 × radian × radius square, It is similar to the triangle area: 1 / 2 × bottom × height. The formula is: s sector = (LR) / 2 (L is the arc length of the sector, R is the radius) s sector = (n / 360) π R ^ 2 (n is the degree of the central angle, R is the radius)
Cone: a solid figure such as a circular cone and a pyramid is a cone. A solid figure obtained by rotating a right edge of a right triangle as an axis for one circle is a cone. A pyramid has three pyramids, four pyramids, five pyramids, six pyramids The volume of the cone is the area of the bottom × the height × 1 / 3. For example, the cone is v = 1 / 3 π R & sup2; h; (R is the radius of the bottom circle, h is the height)

Make a conical funnel with a bus length of 20cm. When you ask the height of the conical funnel, is its volume the largest?
Specific process, thank you!

Let the funnel height be h and the bottom radius be r
h²+r²=20²
h²+(r²/2)+(r²/2)
The volume of cone is v = (1 / 3) π R & sup2; H
v²=(π²/3)×r²×r²×h²
=(π²/12)×(r²/2)×(r²/2)×h²