dprajapati832000
06.03.2022 •
Mathematics
A polyhedra has 37 edges and 15 faces. How many vertices does it have?.
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Ответ:
let n be a considerably large number. the larger n, the closer is the length of ab to the length of the arc ab which is 2πr/n
consider the second picture, the sectors are divided in groups of 2, looking in opposite to each other, forming the parallelogram form as shown.
the 2 parallel horizontal bases are each very close to 2πr/2=πr
the other 2 parallel sides, for a very large number n, are almost equal to the height.
so the height is approximately equal to r
area of parallelogram is base*height=πr*r=
answer: