Question
A rectangular prism has a base area of 15 cm² and a pyramid with a congruent base and height has a volume of 20 cm with the little three what is the height of the rectangular prism
20 cm
4 cm
4/3 cm
5cm
20 cm
4 cm
4/3 cm
5cm
Answers
GPT 3.5
To find the height of the rectangular prism, we need to first find the base of the pyramid.
Since the base area of the rectangular prism is 15 cm², the base of the pyramid will also have an area of 15 cm².
Let's assume the base of the pyramid is a square with side length x. The area of the square is x².
Given that x² = 15 cm², we can solve for x:
x = √15 cm
Now, we know that the volume of the pyramid is given by 1/3 * base area * height. In this case, the volume is given as 20 cm³ and the base area is 15 cm². Therefore, we can solve for the height:
20 = (1/3) * 15 * h
h = 20 / (1/3 * 15)
h = 4 cm
So, the height of the rectangular prism is 4 cm.
Since the base area of the rectangular prism is 15 cm², the base of the pyramid will also have an area of 15 cm².
Let's assume the base of the pyramid is a square with side length x. The area of the square is x².
Given that x² = 15 cm², we can solve for x:
x = √15 cm
Now, we know that the volume of the pyramid is given by 1/3 * base area * height. In this case, the volume is given as 20 cm³ and the base area is 15 cm². Therefore, we can solve for the height:
20 = (1/3) * 15 * h
h = 20 / (1/3 * 15)
h = 4 cm
So, the height of the rectangular prism is 4 cm.