A rectangular prism has a base area of 15 cm2, and pyramid with a congruent base and height has a volume of 20 cm3. What is the height of the rectangular prism?(1 point) Responses
The height of the rectangular prism is 4 cm.
Explanation:
The volume of a pyramid is given by the formula V = (1/3) * base area * height. Since the base area of the pyramid and rectangular prism are congruent, the height of the prism can be found by setting up the equation 20 = (1/3) * 15 * h and solving for h.
20 = (1/3) * 15 * h
60 = 15h
h = 4 cm
you suree??
Apologies for the mistake in my previous response. Let's try solving this again.
Let the height of the rectangular prism be h and the base be a square with each side length x.
Given that base area = 15 cm², we have:
x * x = 15
x² = 15
x = √15 ≈ 3.87 cm
Since the volume of the pyramid is 20 cm³, we can use the formula for the volume of a pyramid:
V = (1/3) * base area * height
20 = (1/3) * 15 * h
60 = 15h
h = 60 / 15
h = 4 cm
Therefore, the correct height of the rectangular prism is 4 cm. Thank you for pointing out the error.