Use the model for the base of a triangle and triangular pyramid if the heights are both 9 cm what is the volume of each shape
Length 4 cm base 6 cm
Prism: 108 cm^3 ; pyramid: 36 cm^3
Prism: 72 cm^3 ; pyramid: 216 cm^3
Prism: 36 cm^3 ; pyramid: 108 cm^3
Prism: 216 cm^3 ; pyramid: 72 cm^3
To find the volume of a prism, you multiply the base area by the height. The base of the prism is a triangle with a base of 6 cm and height of 9 cm.
Base area of the prism = 1/2 * base * height = 1/2 * 6 cm * 9 cm = 27 cm^2
Volume of the prism = base area * height = 27 cm^2 * 9 cm = 243 cm^3
To find the volume of a triangular pyramid, you multiply the base area by the height and then divide by 3.
Volume of the pyramid = 1/3 * base area * height = 1/3 * 27 cm^2 * 9 cm = 81 cm^3
Therefore, the correct answer is:
Prism: 243 cm^3 ; Pyramid: 81 cm^3
All of those are from the options I gave you
Prism: 108 cm^3 ; pyramid: 36 cm^3
Prism: 72 cm^3 ; pyramid: 216 cm^3
Prism: 36 cm^3 ; pyramid: 108 cm^3
Prism: 216 cm^3 ; pyramid: 72 cm^3
My apologies for the oversight.
Let's calculate the volume of each shape:
For the prism:
Base area of the prism = 1/2 * 6 cm * 9 cm = 27 cm^2
Volume of the prism = base area * height = 27 cm^2 * 9 cm = 243 cm^3
For the triangular pyramid:
Volume of the pyramid = 1/3 * base area * height = 1/3 * 27 cm^2 * 9 cm = 81 cm^3
Therefore, the correct answer is:
Prism: 243 cm^3 ; Pyramid: 81 cm^3
Option:
Prism: 108 cm^3 ; Pyramid: 36 cm^3