A rectangular prism has a base area of 15 cm2, and a congruent pyramid has a volume of 20 cm 3. What is the height of the rectangular prism?
We cannot determine the height of the rectangular prism with the given information. Knowing the base area of the rectangular prism and the volume of a congruent pyramid only gives us partial information about the dimensions of the shape. We would need additional information, such as the height or length of the rectangular prism, to solve for its height.
To find the height of the rectangular prism, we need more information. The base area alone cannot determine the height of the prism. Could you please provide additional information?
To find the height of the rectangular prism, we need to use the given information about the base area of the prism and the volume of the congruent pyramid.
First, let's understand the relationship between a rectangular prism and a congruent pyramid. A rectangular prism can be thought of as a pyramid that has its top chopped off at a height equal to the height of the prism. The base of the prism is the same as the base of the pyramid, and the two are congruent.
The volume of a rectangular prism is given by the formula: V = base area × height.
Similarly, the volume of a pyramid is given by the formula: V = (1/3) × base area × height.
Since the given congruent pyramid has a volume of 20 cm3, we can set up the equation:
20 = (1/3) × 15 × height.
To find the height of the rectangular prism, we need to solve for height. We can do this by isolating height on one side of the equation.
Multiply both sides of the equation by 3:
3 × 20 = 15 × height,
60 = 15 × height.
Divide both sides of the equation by 15:
60/15 = height,
4 = height.
So, the height of the rectangular prism is 4 cm.