The base of a solid is the region enclosed by an ellipse having the equation 3x^2 +y^2 = 6. find the volume of the solid if all cross sections by a plane perpendicular to the x axis are squares

Step-by-step explanation:

we know that

If the base of the solid is a circle and all plane sections perpendicular to a fixed diameter of the base are equilateral triangles

then

The solid is a cone

The volume of a cone is equal to

we have

Find out the height of the cone

Remember that

If all plane sections perpendicular to a fixed diameter of the base are equilateral triangles

then

The length side of each equilateral triangle is equal to the diameter of the base

Applying the Pythagoras Theorem find out the height of the cone

we have

----> the diameter is two times the radius

substitute and solve for h

Find the volume

assume

step-by-step explanation:

answer: 0.26

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