A machine assembly requires two pyramid-shaped parts. One of the pyramids has the dimensions shown in the figure. The other pyramid is a scaled version of the first pyramid with a scale factor of 4. What is the volume of the larger pyramid?
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Given:
A machine assembly requires two pyramid-shaped parts.
One of the pyramids has the dimensions shown in the figure.
The other pyramid is a scaled version of the first pyramid with a scale factor of 4.
To find:
What is the volume of the larger pyramid?
Solution:
From attached figure, we have,
The length of rectangular pyramid = 3 units
The width of rectangular pyramid = 2 units
The height of rectangular pyramid = 6 units
scale factor = 4
Therefore, the dimensions are given as follows:
length = 3 × 4 = 12 units
width = 2 × 4 = 8 units
height = 6 × 4 = 24 units
Volume of a rectangular pyramid = V = (l × w × h) / 3
V = (12 × 8 × 24) / 3
V = 2304 / 3
∴ V = 768 cubic units
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