Solution:
We know that a Pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. A right pyramid has its apex directly above the centroid of its base. A pyramid that has a regular polygon base is called a regular pyramid.The volume of pyramid is given with b as the area of the base and h as the height of from the base to the apex also is given as
.
We are given the question that the base of a right pyramid is a regular hexagon whose area is 243 square cm which means b = 243 square cm. The area of a side face of the pyramid is 46 square cm. We draw the rough figure of it below with O as the apex and ABCDEF as the base of a regular hexagonal base.
Here l is the slant height dropped from apex on one of the sides (Here OH). The line segment GH is called apothem whose length we denote as pp. We know that area of regular hexagon with side a is 6 times the area of equilateral triangle with side aa which means
. So we have;We observe the triangle OEF which is a die face of the pyramid with slant height
and base . We are given its area as . So we have;
We can find the apothem as the height of equilateral triangle EGF as
We use Pythagoras theorem in right angled triangle OGH to have;
So the volume of pyramid cubic is
