Question

Consider this square pyramid. Recall the volume can be found using the formula V = 1/3Bh.

Answer 1

Answer:

Option A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.

Step-by-step explanation:

step 1

Find the volume of the original pyramid

The volume of the pyramid is equal to

$V=\frac{1}{3}Bh$

where

B is the area of the base

h is the height of the pyramid

we have

$B=16^{2}=256\ m^{2}$ ----> is the area of a square

$h=12\ m$

substitute

$V=\frac{1}{3}(256)(12)$

$V=1,024\ m^{3}$

step 2

Find the volume of the new pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z -------> the scale factor

x ------> the volume of the new pyramid

y -----> the volume of the original pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{1}{4}$

$y=1,024\ m^{3}$

substitute and solve for x

$(\frac{1}{4})^{3}=\frac{x}{1,024}$

$x=(1,024)\frac{1}{64}=16\ m^{3}$

therefore

The volume of the new pyramid is the volume of the original pyramid times 1/64