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 4 cm 4 cm 20 cm 20 cm 4/3 cm Start Fraction 4 over 3 End Fraction cm 5 cm
To find the height of the rectangular prism, we first need to find the dimensions of the base of the pyramid. Since the base area of the rectangular prism is 15 cm^2, and the base of the pyramid is congruent to the base of the prism, the base of the pyramid also has an area of 15 cm^2.
Let's assume the base of the pyramid is a square with side length x. Therefore, the area of the base of the pyramid is x^2 = 15 cm^2. Solving for x, we get:
x^2 = 15
x = √15 ≈ 3.87 cm
Since the pyramid has a volume of 20 cm^3, its volume formula is:
V = (1/3) * base area * height
20 = (1/3) * 15 * h
20 = 5h
h = 20 / 5
h = 4 cm
Therefore, the height of the rectangular prism is 4 cm.