For similar solids, the ratio of surface areas equals the square of the linear scale factor $k^2$. ЅAТ рrеp bу⁠ Anікo.‌ai

Once you have $k$, scale the volume of pyramid A by $k^3$ (not by $k$ or $k^2$).

In Desmos, define s=6 and h=4. Then enter l=sqrt((s/2)^2+h^2) and SAa=s^2+2*s*l.

Enter SAb=480 and k=sqrt(SAb/SAa). Аni‌ko​ - ‌Frеe ЅA​Т Prep This uses $k^2=\frac{SA_B}{SA_A}$.

Enter Va=(1/3)*s^2*h and Vb=Va*k^3. Compare the expression shown for Vb to the answer choices and select the match.

For a right square pyramid with base side length $s$ and height $h$, the slant height $\ell$ of a face comes from a right triangle with legs $h$ and $\frac{s}{2}$:

With $s=6$ and $h=4$:

Total surface area (including base) is

So

Since the pyramids are similar, if the linear scale factor from A to B is $k$, then surface areas scale by $k^2$:

Con​tent bу Anіk‌ο.‌ai

So $k=\sqrt{5}$. (Use the positive root because lengths are positive.)

First find the volume of pyramid A:

Volumes scale by $k^3$, so

So the correct choice is $240\sqrt{5}$.