Urgent! ! Calculation method for finding the arc surface expansion of vase. The score is not much, I hope to have friends who know about it to help! thank you

Let the central angle of the vase side be θ, the radius of the inner arc be r, the radius of the outer arc be r, and the width of the unfolding ring be h.

According to the arc length formula:

rθ=53.5

Rθ=7 1.4

Because the height of the bottle is 4cm, the upper bottom diameter 17cm and the lower bottom diameter is 22.7cm, the Pythagorean theorem is used: h = √ {[(22.7-17)/2] 2+42} ≈ 4.91(cm).

Where R-r≈4.9 1

The simultaneous solutions of the three formulas are: θ≈3.65, r≈ 14.66, R≈ 19.56.

According to the sector area formula:

The side area of the vase = (θ r 2-θ r 2)/2.

=(7 1.4R-53.5r)/2

≈(7 1.4* 19.56-53.5* 14.66)/2

=306. 137(cm^2)

That is, the area of the vase development diagram is about 306. 137 square centimeters.