Relationship Between Volume of Prisms & Pyramids Practice
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Question
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An illustration shows a triangle with sides measuring 16 meters, 14 meters, and 8 meters. A dashed perpendicular line, from the side measuring 16 meters to the opposite angle, measures 7 meters. A right angle symbol is shown to the left of the perpendicular line.
A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?
(1 point)
The volume of the prism is
m3.
The volume of the pyramid is
m3.
To find the volume of the prism, you first need to find the area of the triangle base by using the formula for the area of a triangle (1/2 * base * height). The base of the triangle is 14 meters and the height of the triangle is 7 meters (from the perpendicular line). So, the area of the triangular base is 1/2 * 14 * 7 = 49 square meters.
Then, you multiply the area of the base by the height of the prism to find the volume. The height of the prism is 15 meters. So, the volume of the prism is 49 * 15 = 735 cubic meters.
To find the volume of the pyramid, you use the same formula, but you divide the result by 3 since the volume of a pyramid is 1/3 * base area * height. So, the volume of the pyramid is 49 * 15 / 3 = 245 cubic meters.
Therefore, the volume of the prism is 735 cubic meters and the volume of the pyramid is 245 cubic meters.