Question

Please no links or files I need a direct answer.

Answer 1

Answer:

$\text{a. }128\:\mathrm{cm^3},\\\text{b. }4:1,\\\text{c. }179.4\:\mathrm{cm^2};\:44.8\:\mathrm{cm^2}$

Step-by-step explanation:

The volume of a square pyramid is given by $V=\frac{1}{3}\cdot s^2\cdot h$

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 $2^3=8$ times larger than the volume of pyramid B.

Thus, the volume of pyramid A is equal to $16\cdot 8=\boxed{128\:\mathrm{in^3}}$. 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 $2^2:1=\boxed{4:1}$

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 $2s\sqrt{\left(\frac{s}{2}\right)^2+h^2}+s^2$ for a square pyramid with base edge $s$ and height $h$.

Plugging in values, we get the following:

$A_a\approx \boxed{179.4\:\mathrm{cm^2}},\\A_b\approx \boxed{44.8\:\mathrm{cm^2}}$