A rectangular pyramid has a volume of 10 cm3 . What is the volume of a rectangular prism given it has a congruent base and height to the pyramid?
Since the rectangular prism has a congruent base and height to the rectangular pyramid, they are similar shapes and have the same dimensions.
Therefore, the volume of the rectangular prism is also 10 cm3.
Incorrect
Apologies for the error in my previous response.
Let's start by finding the volume of the rectangular pyramid using the formula:
Volume = (1/3) * base area * height
Given that the volume of the rectangular pyramid is 10 cm3, and the base area is b and the height is h, we have:
10 = (1/3) * b * h
Now, for a rectangular prism that has a congruent base and height to the pyramid, its volume can be calculated using the formula:
Volume = base area * height
Since the base area of the rectangular prism would also be b (same as the base area of the pyramid), the volume of the rectangular prism will be:
Volume = b * h
From the equation we derived earlier for the pyramid, we have:
10 = (1/3) * b * h
Multiplying by 3 to get rid of the fraction:
30 = b * h
Therefore, the volume of the rectangular prism is 30 cm3.