The difference betwen the volume of the new pyramid and the volume of the original pyramid gives the increase in the volume of the pyramid which is 6 [tex]\rm cm^3[/tex].
Given :
- Length of the pyramid is 3 cm.
- Width of the pyramid is 3cm.
- Height of the pyramid is 5 cm.
- the slant height of the pyramid increases by 4 centimeters and its height increases by 2 centimeters.
Original volume of the pyramid will be:
[tex]\rm Volume = \dfrac{1}{3}(L\times W\times H)[/tex]
[tex]\rm Volume = \dfrac{1}{3}(3\times3\times 5)[/tex]
Volume = 15 [tex]\rm cm^3[/tex]
After the increase in 4cm of slant height of the pyramid and 2 cm increase in height, the volume of the new pyramid becomes:
[tex]\rm V' = \dfrac{1}{3}\times (L)\times (W)\times (H+2)[/tex]
[tex]\rm V' = \dfrac{1}{3}(3\times3\times7)[/tex]
V' = 21 [tex]\rm cm^3[/tex]
Therefore, the volume of the pyramid increases by (21 - 15 = 6) cubic centimeters.
For more information, refer the link given below:
https://brainly.com/question/23409099
