14 m

Question

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?

Answer 1

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

Answer 2

prism: 840

pyramid: 280

Answer 3

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