Answer: To compute the volume of a prism, we need to know the area of the base and the height of the prism. Assuming that the prism has a rectangular base, the formula for the volume of the prism is:
Volume = Area of Base × Height
Let's assume that the length and width of the rectangular base are both equal to 2d (since we don't have specific dimensions). The height of the prism is also equal to d, as given.
When d = 1:
The area of the base is 2d × 2d = 4 square units
The height is d = 1 unit
Therefore, the volume is:
Volume = Area of Base × Height = 4 × 1 = 4 cubic units
When d = 2:
The area of the base is 2d × 2d = 8 square units
The height is d = 2 units
Therefore, the volume is:
Volume = Area of Base × Height = 8 × 2 = 16 cubic units
When d = 1/2:
The area of the base is 2d × 2d = 1 square unit
The height is d = 1/2 unit
Therefore, the volume is:
Volume = Area of Base × Height = 1 × (1/2) = 1/2 cubic units
So, the volume of the prism is 4 cubic units when d=1, 16 cubic units when d=2, and 1/2 cubic units when d=1/2.
Explanation: