Question
A rectangular prism has a base area of 15 cm^2, and pyramid with a congruent base and height has a volume of 20 cm^3. What is the height of the rectangular prism?
Answers
GPT 3.5
To find the height of the rectangular prism, we first need to determine the dimensions of the base of the prism.
Since the base area of the rectangular prism is 15 cm^2 and the base of the pyramid is congruent in shape and size, the base of the pyramid has an area of 15 cm^2.
Let's assume the base of the pyramid has a length and width of x cm each.
Therefore, x * x = 15
x^2 = 15
x = √15
x ≈ 3.87 cm
Now, using the volume formula of a pyramid, V = (1/3) * base area * height, we can calculate the height of the pyramid.
20 = (1/3) * 15 * h
20 = 5h
h = 4 cm
Therefore, the height of the rectangular prism is also 4 cm.
Since the base area of the rectangular prism is 15 cm^2 and the base of the pyramid is congruent in shape and size, the base of the pyramid has an area of 15 cm^2.
Let's assume the base of the pyramid has a length and width of x cm each.
Therefore, x * x = 15
x^2 = 15
x = √15
x ≈ 3.87 cm
Now, using the volume formula of a pyramid, V = (1/3) * base area * height, we can calculate the height of the pyramid.
20 = (1/3) * 15 * h
20 = 5h
h = 4 cm
Therefore, the height of the rectangular prism is also 4 cm.