Question

Can you please help me out with a question

Answer 1

Given the lengths of the squares of the two pyramids to be in ratio

`4in\colon12in=1in\colon3in`

This implies that the volumes of the small pyramid and the large pyramid will be in the ratio

`1^3in^3\colon3^3in^3=1in^3\colon27in^3`

Given the volume of a pyramid formula to be

`V=(1)/(3)* base\text{ area}* height`

for the small pyramid of base has length of 4inches and height 6 inches

`\begin{gathered} \text{base area=l}^2 \\ l=4in \\ \text{base area=4}^2=16in^2 \\ V=(1)/(3)*16*6=(96)/(3) \\ =32in^3 \end{gathered}`

Since the small square based pyramid is in the ratio of 1 : 27 to the large square based pyramid, then

`\begin{gathered} \text{the volume of the larger pyramid is} \\ V_l=32*27=864in^3 \end{gathered}`

Therefore, the volume of the larger pyramid is 864 in³

Option G is right choice