Step-by-step explanation:
The volume of a square pyramid is given by
Since pyramids A and B are similar, their corresponding side lengths are proportion. Since the base edge of B is half that of A's, each dimension of B will be half of A. Since the formula for volume requires the multiplication of three dimensions, the volume of pyramid A will be times larger than the volume of pyramid B.
Thus, the volume of pyramid A is equal to . You can also find the dimensions of pyramid A and use the formula.
The surface area consists of the sum of all areas of the 2D shapes that make the figure. Since all dimensions of pyramid A are twice the dimensions of pyramid B, the ratio of the surface area of pyramid A to pyramid B is
The surface area of a square pyramid can be found by adding the areas of the three triangles and one square that make it up. As one long messy formula, that becomes for a square pyramid with base edge and height .
Plugging in values, we get the following: