The volume of a prism is given by the formula V = base area x height. Since the base of the prism is a triangle with sides 16m, 14m, and 8m, we can calculate the area using Heron's formula:
s = (16 + 14 + 8) / 2 = 19
Area = √(19(19-16)(19-14)(19-8)) = √(19*3*5*11) = √3135 ≈ 56.03 m²
Then, the volume of the prism is V = 56.03 m² x 15 m = 840.45 m³
The volume of a pyramid is given by V = (1/3) x base area x height. Since the base of the pyramid is also a triangle with sides 16m, 14m, and 8m, the area remains 56.03 m².
Therefore, the volume of the pyramid is V = (1/3) x 56.03 m² x 15 m = 280.23 m³.
Use the image to answer the question.
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
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The volume of the pyramid is
m3
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2 answers
this is wrong