Respuesta :
Given the lengths of the squares of the two pyramids to be in ratio
[tex]4in\colon12in=1in\colon3in[/tex]This implies that the volumes of the small pyramid and the large pyramid will be in the ratio
[tex]1^3in^3\colon3^3in^3=1in^3\colon27in^3[/tex]Given the volume of a pyramid formula to be
[tex]V=\frac{1}{3}\times base\text{ area}\times height[/tex]for the small pyramid of base has length of 4inches and height 6 inches
[tex]\begin{gathered} \text{base area=l}^2 \\ l=4in \\ \text{base area=4}^2=16in^2 \\ V=\frac{1}{3}\times16\times6=\frac{96}{3} \\ =32in^3 \end{gathered}[/tex]Since the small square based pyramid is in the ratio of 1 : 27 to the large square based pyramid, then
[tex]\begin{gathered} \text{the volume of the larger pyramid is} \\ V_l=32\times27=864in^3 \end{gathered}[/tex]Therefore, the volume of the larger pyramid is 864 in³
Option G is right choice
