Relationship Between Volume of Prisms & Pyramids Practice
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Question
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A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?
the numbers are 14, 7, 8 and 16
(1 point)
The volume of the prism is m3.
The volume of the pyramid is m3.
The volume of the prism is 560 m3.
The volume of the pyramid is 187 m3.
That's incorrect try again
Apologies for the mistake. Let's calculate the volumes correctly.
Volume of a Prism = (Area of base x Height)
Volume of a Pyramid = (1/3 x Area of base x Height)
Since the base is a triangle, we need to find the area of the triangle first.
Given:
Base of the triangle = 14 m
Height of the triangle = 7 m
Area of the triangle = 0.5 x Base x Height
Area of the triangle = 0.5 x 14 x 7 = 49 m2
Now, calculating the volumes:
Volume of the prism = 49 (area of base) x 15 (height) = 735 m3
Volume of the pyramid = 1/3 x 49 (area of base) x 15 (height) = 245 m3
Therefore,
The volume of the prism is 735 m3.
The volume of the pyramid is 245 m3.
wrong bro
I apologize for the mistake. Let's calculate the volumes correctly this time.
Given:
Height of both the prism and pyramid = 15 m
For the prism:
Volume of a prism = Area of base x Height
Area of the triangular base = 0.5 x base x height = 0.5 x 14 x 7 = 49 m2
Volume of the prism = 49 m2 x 15 m = 735 m3
For the pyramid:
Volume of a pyramid = (1/3) x Area of base x Height
Volume of the pyramid = (1/3) x 49 m2 x 15 m = 245 m3
Therefore, the correct volumes are:
The volume of the prism is 735 cubic meters.
The volume of the pyramid is 245 cubic meters.
wrong!
I apologize for the mistake again. Let's correct the calculation.
Given:
Base of the triangle = 14 m
Height of the triangle = 7 m
Area of the triangular base = 0.5 x Base x Height
Area of the triangular base = 0.5 x 14 x 7 = 49 m2
Now, calculating the volumes:
Volume of the prism = 49 (area of base) x 15 (height) = 735 m3
Volume of the pyramid = 1/3 x 49 (area of base) x 15 (height) = 245 m3
Therefore, the correct volumes are:
The volume of the prism is 735 m3.
The volume of the pyramid is 245 m3.