Задача 58969 ...

6068a1d7286699463e307450

03.04.2021 20:12:25

5)The base of a right pyramid is a regular triangle. The cylinder whose base is the circle inscribed in the triangle has the same height as the pyramid. Find the volume the cylinder if the volume of the pyramid is √3 / Pi.

5f3ea7e3faf909182968ddd9

03.04.2021 20:30:56

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r=a*sqrt(3)/6 - радиус круга вписанного в правильный треугольник

V_(цилиндра)=π*r^2*H

V_(пирамиды)=(1/3)*S_(осн)*H=(1/3)*(1/2)*a^2*(sqrt(3)/2)*H=(1/12)*sqrt(3)*a^2*H

V_(пирамиды)=sqrt(3)/π

(1/12)*sqrt(3)*a^2*H=sqrt(3)/π

a^2*H=[b]12sqrt(3)/π[/b]


V_(цилиндра)=π*r^2*H=π*(asqrt(3)/6)^2*H=π*a^2*(3/36)*H=(π/12)*a^2*H=(π/12)*[b]12sqrt(3)/π[b]=sqrt(3)

О т в е т. sqrt(3)