Answer:
The volume of pyramid A is twice of pyramid B and if the height of pyramid B increased to twice that of pyramid A, the new volume of pyramid B is the equal to the volume of pyramid A.
Step-by-step explanation:
Given information:
Pyramid A: Rectangular base of 10×20.
Pyramid B: Square base of 10×10.
It is given that
The volume of a pyramid is the heights of the pyramids are the same.
Let the height of both pyramids be h.
![V=\frac{1}{3}Bh](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7DBh)
Where, B is base area and h is height of the pyramid.
The volume of Pyramid A is
![V_A=\frac{1}{3}(10\times 20)h](https://tex.z-dn.net/?f=V_A%3D%5Cfrac%7B1%7D%7B3%7D%2810%5Ctimes%2020%29h)
![V_A=\frac{200}{3}h](https://tex.z-dn.net/?f=V_A%3D%5Cfrac%7B200%7D%7B3%7Dh)
The volume of Pyramid B is
![V_B=\frac{1}{3}(10\times 10)h](https://tex.z-dn.net/?f=V_B%3D%5Cfrac%7B1%7D%7B3%7D%2810%5Ctimes%2010%29h)
![V_B=\frac{100}{3}h](https://tex.z-dn.net/?f=V_B%3D%5Cfrac%7B100%7D%7B3%7Dh)
We conclude that,
![\frac{200}{3}h=2\times \frac{100}{3}h](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7B3%7Dh%3D2%5Ctimes%20%5Cfrac%7B100%7D%7B3%7Dh)
![V_A=2\times V_B](https://tex.z-dn.net/?f=V_A%3D2%5Ctimes%20V_B)
It means the volume of pyramid A is twice of pyramid B.
Now, the height of pyramid B increased to twice that of pyramid A.
Let the height of pyramid B is 2h and height of pyramid a is h.
![V_A=\frac{1}{3}(10\times 20)h](https://tex.z-dn.net/?f=V_A%3D%5Cfrac%7B1%7D%7B3%7D%2810%5Ctimes%2020%29h)
![V_A=\frac{200}{3}h](https://tex.z-dn.net/?f=V_A%3D%5Cfrac%7B200%7D%7B3%7Dh)
The volume of Pyramid B is
![V_B=\frac{1}{3}(10\times 10)2h](https://tex.z-dn.net/?f=V_B%3D%5Cfrac%7B1%7D%7B3%7D%2810%5Ctimes%2010%292h)
![V_B=\frac{200}{3}h](https://tex.z-dn.net/?f=V_B%3D%5Cfrac%7B200%7D%7B3%7Dh)
![V_B=V_A](https://tex.z-dn.net/?f=V_B%3DV_A)
Therefore the volume of pyramid A is twice of pyramid B and if the height of pyramid B increased to twice that of pyramid A, the new volume of pyramid B is the equal to the volume of pyramid A.