Calculation of the surface area of a round table

Calculation of the surface area of a round table

In order to calculate the surface area of a circular platform, the radius and slant height of the upper and lower bottom surfaces (not the height, but a part of the generatrix) can be calculated as follows
(surface area) = (area of upper and lower circles) + (side area)
＝π(r22+r12)+πl1(r1+r2)
＝π(r1l1+r22+r12+r2l1)
＝π｛r1(l1+r1)+r2(l1+r2)｝
Here, π also plays an important role
Rearrange and write out the calculation formula of volume V and surface area s of the frustum
S＝π〔r1(l1+r1)+r2(l1+r2)〕

How to calculate the surface area of the cone
It is known that the radii of the top and bottom surfaces of the frustum are 1 and 4 respectively, the length of the generatrix is 4, and the surface area of the frustum is? How to find the drop?

Elder brother, you forget that the round platform has upper and lower bottoms!
A cone is cut from a cone. The side of a cone can be calculated by subtracting the side of a small cone from the side of a large cone. It can also be said that the expansion is a part of a sector
S side = (2 π R2 + 2 π R1) * L / 2 = 2 π (1 + 4) * 4 / 2 = 20 π
S up and down = π R2 ^ 2 + π R1 ^ 2 = 17 π
So the surface area of the cone is s = s side + s up and down = 37 π

Calculating the surface area of a round table
The radii of the top and bottom surfaces of the cone are 10cm and 20cm respectively. The center angle of the fan ring in the side unfolded view is 180 ° to calculate the surface area and volume. I don't know how the center angle of the fan ring is 180 ° to form a cone at most,

(1) Calculate the surface area: lower surface area S1 = π R1 ^ 2 = 400 π cm ^ 2; lower surface area S2 = π R2 ^ 2 = 100 π cm ^ 2; the sector on the side is half of a ring, which is also the area of half a big circle minus the area of half a small circle. The arc length of half a big arc is the perimeter of the lower surface circle, L1 = 2 π R1 = 40 π cm

Advanced calculus in University
The difference between ∫ f (x) DX = f (x) + C (C is constant) and ∫ f '(x) DX = f (x) + C (C is constant) in indefinite integral

In the first article, f (x) is the original function of F (x) and f (x) is the derivative of F (x)