A rectangular prism has a base area of 15 centimeters to the second power and pyramid with a congruent base and height has a volume of 20 centimeters to the third power what is the height Of the rectangular prism
4/3 cm
20 cm
5 cm
4 cm
To find the height of the rectangular prism, we first need to find the base dimensions of the pyramid. Since the pyramid has a volume of 20 cm^3 and a congruent base area of 15 cm^2, we can use the formula for the volume of a pyramid:
Volume = (1/3) * base area * height
Substitute in the known values:
20 = (1/3) * 15 * height
Multiply both sides by 3 to solve for height:
60 = 15 * height
Divide by 15:
height = 4 cm
Therefore, the height of the rectangular prism is 4 cm.
Use the model for the base of a triangular prism and triangular pyramid. If the heights are both nine centimeters what is the volume of each shape?
Prism: 36 cm 3 ; pyramid: 108 cm 3
Prism: 108 cm3 ; Pyramid 36 cm3
Prism: 216 cm3 ; pyramid: 72 cm3
prism:72 cm3 ; pyramid: 216 cm3
Given that the height is 9 cm for both shapes and the volume formula for a prism is base area * height and for a pyramid is (1/3) * base area * height, we can calculate the volumes of the prism and the pyramid.
Since the base area is the same for both:
Volume of Prism = base area * height = (base area) * (height) = (1/2 * base * height) * height = (1/2 * base * height) * height = 1/2 * base * height^2 = 1/2 * 36 * 9 = 162 cm^3
Therefore, the volume of the prism is 162 cm^3.
Using the volume formula for a pyramid:
Volume of Pyramid = (1/3) * base area * height = (1/3) * (1/2 * base * height) * height = (1/6) * base * height^2 = (1/6) * 36 * 9 = 54 cm^3
Therefore, the volume of the pyramid is 54 cm^3.
Therefore, the correct answer is: Prism: 162 cm^3; Pyramid: 54 cm^3.