**a solid has a circular base of radius 20cm. find the volume of the solid if every plane section perpendicular to a certain diameter is an equilateral triangle**

**Answer:**

If every plane section perpendicular to a certain diameter is an equilateral triangle, then it means that solid is a cone.

In this solid cone every plane section perpendicular to a certain diameter will have two of it’s sides always equal to each other and equal to slant height of the cone. Since the plane sections in the question are equilateral triangles, Hence it’s slant height are equal to it’s diameter.

Now the height of the cone can be calculated from the right triagnle made by slant height (hypotenuse) and radius (base) and height of cone (height)

And the height of the cone is:

h = 3–√r = 34.641 cm

And volume of the cone is :