A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?
Actually the correct answer is:
The volume of the prism is 840
the volume of the pyramid is 280
The volume of a prism is given by the formula:
Volume = Base Area x Height
Since the base of the prism and pyramid are congruent, the base area will be the same for both shapes. The base area of a triangle is given by:
Base Area = (1/2) x base x height
Given that the height of the triangle is 15 m, we need to find the base of the triangle. To do this, we need additional information about the triangle, such as the lengths of the sides or the angles. Without this information, we cannot calculate the volume of the prism or pyramid.
14m
7m
8m
Great, with the base of the triangle provided, we can calculate the volume of both shapes.
For the prism:
Base Area = (1/2) x base x height
Base Area = (1/2) x 14m x 15m
Base Area = 105 m²
Volume of prism = Base Area x Height
Volume of prism = 105m² x 15m
Volume of prism = 1575 m³
For the pyramid:
Volume of pyramid = (1/3) x Base Area x Height
Volume of pyramid = (1/3) x 105m² x 15m
Volume of pyramid = 525 m³
Therefore, the volume of the prism is 1575 cubic meters and the volume of the pyramid is 525 cubic meters.