The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same. The volume of pyramid A is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is the volume of pyramid A.

Answer:Part 1) The volume of pyramid A is two times the volume of pyramid BPart 2) The new volume of pyramid B is equal to the volume of pyramid AStep-by-step explanation:we know thatThe volume of a pyramid is equal to[tex]V=\frac{1}{3}Bh[/tex]whereB is the area of the base of pyramidh is the height of the pyramidPart 1The heights of the pyramids are the same Find the volume of pyramid AFind the area of the base B[tex]B=10*20=200\ m^{2}[/tex]substitute[tex]VA=\frac{1}{3}(200)h[/tex][tex]VA=\frac{200}{3}h\ m^{3}[/tex]Find the volume of pyramid BFind the area of the base B[tex]B=10^{2}=100\ m^{2}[/tex]substitute[tex]VB=\frac{1}{3}(100)h[/tex][tex]VB=\frac{100}{3}h\ m^{3}[/tex]Compare the volumes[tex]VA=2VB[/tex]The volume of pyramid A is two times the volume of pyramid BPart 2) If the height of pyramid B increases to twice that of pyramid Awe have that[tex]VA=\frac{200}{3}h\ m^{3}[/tex]Find the new volume of pyramid Bwe have[tex]B=100\ m^{2}[/tex][tex]h=2h\ m[/tex]substitute[tex]VB=\frac{1}{3}(100)(2h)[/tex][tex]VB=\frac{200}{3}h\ m^{3}[/tex]Compare the volumes[tex]VA=VB[/tex]The new volume of pyramid B is equal to the volume of pyramid A