Use the image to answer the question. A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?
The volume of the prism is _____, m3.
The volume of the pyramid is _____, m3.
wrong
The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height.
For the prism, the base is a triangle with area 1/2 * 6 * 8 = 24 m^2. Therefore, the volume of the prism is V = 24 * 15 = 360 m^3.
The volume of a pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height.
For the pyramid, the base is also a triangle with area 24 m^2. Therefore, the volume of the pyramid is V = (1/3) * 24 * 15 = 120 m^3.
Apologies for the error, let's correct the calculations:
Since the prism and pyramid have a congruent triangular base, we can assume the base of each shape is a right-angled triangle with base 8m and height 6m (half of an 8x6 rectangle). The Area of the base (triangle) is 1/2 * base * height = 1/2 * 8 * 6 = 24 square meters.
1. Volume of the prism:
Volume of prism = Base Area x Height = 24 m^2 x 15 m = 360 cubic meters.
2. Volume of the pyramid:
Volume of pyramid = (1/3) x Base Area x Height = (1/3) x 24 m^2 x 15 m = 120 cubic meters.