Relationship Between Volume of Prisms & Pyramids Practice
1. A rectangular prism has a volume of 48 cubic units. If each side is doubled in length, what will be the new volume of the prism?
Solution: Since the volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height, the new volume of the prism with each side doubled will be:
V = (2l)(2w)(2h) = 8(lwh) = 8(48) = 384 cubic units
Therefore, the new volume of the prism will be 384 cubic units.
2. A square pyramid has a volume of 36 cubic units. If the height of the pyramid is tripled, what will be the new volume of the pyramid?
Solution: Since the volume of a pyramid is given by V = (1/3)Bh, where B is the base area and h is the height, tripling the height will result in:
V = (1/3)B(3h) = B*h
Since the volume of the pyramid is 36 cubic units, the base area (B) can be calculated by multiplying the volume by 3 and the height:
36 * 3 = B*3h
B = 36 unit^2
The new volume of the pyramid with the height tripled will be:
V = 36 * 3h = 108 cubic units
Therefore, the new volume of the pyramid will be 108 cubic units.