He volume of the pyramid shown in the figure is cubic centimeters. if the slant height of the pyramid increases by 4 centimeters and its height increases by 2 centimeters, the volume of the pyramid increases by cubic centimeters.

Part a) The volume of the original pyramid is

Part b) The volume of the pyramid increases by  

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

where

B is the area of the base

h is the height of pyramid

see the attached figure to better understand the problem

Step 1

Find the volume of the original pyramid

the area of the base B is equal to

substitute

Step 2

Find the volume of the new pyramid

-------> the area of the base is the same

------> the height increase by

substitute

Subtract the original volume from the new volume

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363