A circular cylinder with a volume of 8$\pi $ ${m}^{3}$ is circumscribed about a right prism whose base is an equilateral triangle with one side that measures 2m. what is the altitude of the cylinder.

pominjaneh6
2022-08-08
Answered

A circular cylinder with a volume of 8$\pi $ ${m}^{3}$ is circumscribed about a right prism whose base is an equilateral triangle with one side that measures 2m. what is the altitude of the cylinder.

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wietselau

Answered 2022-08-09
Author has **28** answers

so you need to know that in one equilateral triangle one degree mesure is 60 and the bisectores are heights and again you need to know that those heights where will intersected so this point will be the central point of this circule what is the base of this cylinder

we know again that those heights (bisectores) part in report $\frac{2}{3}$ +$\frac{1}{3}$ so that the $\frac{2}{3}$ part of one bisector will be equal with r from this circle

so we know that one side equal

$2m\mathrm{cos}30=\frac{h}{2}\sqrt{\frac{3}{2}}=\frac{h}{2}h=\sqrt{3}$ from this result that r= $2\sqrt{\frac{3}{3}}$

so the height of cylinder being H and we know that the volum of cylinder is 8$\pi $ m3 and we know that the volum of one cylinder is equal with area of base multiply the height of cylinder

area of base is $\pi $r2 = $\pi $($\frac{4}{3}$)

V=$8\pi $

V=$\pi $($\frac{4}{3}$)H

8$\pi $=$\pi $($\frac{4}{3}$)H

8=($\frac{4}{3}$)H

H= 8($\frac{3}{4}$)

H= $\frac{24}{4}$

H=6 m

we know again that those heights (bisectores) part in report $\frac{2}{3}$ +$\frac{1}{3}$ so that the $\frac{2}{3}$ part of one bisector will be equal with r from this circle

so we know that one side equal

$2m\mathrm{cos}30=\frac{h}{2}\sqrt{\frac{3}{2}}=\frac{h}{2}h=\sqrt{3}$ from this result that r= $2\sqrt{\frac{3}{3}}$

so the height of cylinder being H and we know that the volum of cylinder is 8$\pi $ m3 and we know that the volum of one cylinder is equal with area of base multiply the height of cylinder

area of base is $\pi $r2 = $\pi $($\frac{4}{3}$)

V=$8\pi $

V=$\pi $($\frac{4}{3}$)H

8$\pi $=$\pi $($\frac{4}{3}$)H

8=($\frac{4}{3}$)H

H= 8($\frac{3}{4}$)

H= $\frac{24}{4}$

H=6 m

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