Mathematics: The base of a solid is the circle x^2 +y^2=9 and each cross section perpendicular to the x-axis is an equilateral triangle with one side across the base. find the volume of the solid.

The base of a solid is the circle x^2 +y^2=9 and - id2294327877, callmedarthvadorplz

Ответ:

hdhdjjdj80HDjdjdj

13.01.2022

First, recall that the area of an equilateral triangle with side length

is $\dfrac{\sqrt3}4s^2$ .

Now, each cross section's base is the distance from the top half of the circular base to the lower half. You have

$x^2+y^2=9\iff y=\pm\sqrt{9-x^2}$

This means the vertical distance is $\sqrt{9-x^2}-(-\sqrt{9-x^2})=2\sqrt{9-x^2}$ .

So, the volume of such a solid is given by

$\displaystyle\frac{\sqrt3}4\int_{-3}^3\left(2\sqrt{9-x^2}\right)^2\,\mathrm dx=2\sqrt3\int_0^3(9-x^2)\,\mathrm dx=36\sqrt3$

where the first equality comes from the fact that the circle is symmetric across the y axis.

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Ответ:

mountainwilson

07.07.2020

Mathematics

yeah

Step-by-step explanation:

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The base of a solid is the circle x^2 +y^2=9 and each cross section perpendicular to the x-axis is an equilateral triangle with one side across the base. find the volume of the solid.

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