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.
Given: Pyramid A: Base is rectangle with length of 10 meters and width of 20 meters. Pyramid B: Base is square with 10 meter sides. Heights are the same.
Volume of rectangular pyramid = (L * W * H) / 3 Volume of square pyramid = a² * h/3
Let us assume that the height is 10 meters. V of rectangular pyramid = (10m * 20m * 10m)/3 = 2000/3 = 666.67 m³ V of square pyramid = (10m)² * 10/3 = 100m² * 3.33 = 333.33 m³
The volume of pyramid A is TWICE the volume of pyramid B.
If the height of pyramid B increases to twice the of pyramid A, (from 10m to 20m),
V of square pyramid = (10m)² * (10*2)/3 = 100m² * 20m/3 = 100m² * 6.67m = 666.67 m³
The new volume of pyramid B is EQUAL to the volume of pyramid A.
