Question

Instructions:Select the correct answer from each drop-down menu.

Answer 1

Answer:

Part a) The volume of the original pyramid is $15\ cm^{3}$

Part b) The volume of the pyramid increases by  $6\ cm^{3}$

Step-by-step explanation:

we know that

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 pyramid

Step 1

Find the volume of the original pyramid

the area of the base B is equal to

$B=3^{2}=9\ cm^{2}$

$h=5\ cm$

substitute

$V=\frac{1}{3}(9)(5)=15\ cm^{3}$

Step 2

Find the volume of the new pyramid

$B=9\ cm^{2}$ -------> the area of the base is the same

$h=5+2=7\ cm$ ------> the height increase by $2\ cm$

substitute

$V=\frac{1}{3}(9)(7)=21\ cm^{3}$

Subtract the original volume from the new volume

$21\ cm^{3}-15\ cm^{3}=6\ cm^{3}$

Answer 2

The volume is 10 cubic meters  is 6 cenemeters