14 m
16 m
8 m
7 m
a prism and pyramid have congruent triangular bases. If their heights are both 15 m what is the volume of each shape?
prism: 840
pyramid: 280
I apologize for the confusion in my previous response. The correct volume calculations are as follows:
Volume of the prism = Base Area * Height = 56.02 sq.m * 15 m = 840.3 cubic meters
Volume of the pyramid = (1/3) * Base Area * Height = (1/3) * 56.02 sq.m * 15 m = 280.1 cubic meters
Therefore, the correct volumes are:
Prism: 840 cubic meters
Pyramid: 280 cubic meters
Volume of the prism = Base Area * Height
Volume of the pyramid = (1/3) * Base Area * Height
Given that the height of both shapes is 15m, we need to find the area of the triangular base first.
Let's consider the triangle with sides 14m, 16m, and 8m.
Using Heron's formula,
Semi-perimeter (s) = (14 + 16 + 8) / 2 = 19
Area = √(19 * (19-14) * (19-16) * (19-8)) = √(19 * 5 * 3 * 11) = √3135 ≈ 56.02 sq.m
Now,
Volume of the prism = 56.02 * 15 = 840.3 cubic meters
Volume of the pyramid = (1/3) * 56.02 * 15 = 280.1 cubic meters