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navik [9.2K]
3 years ago
5

What is the scale factor of two similar pyramids with volume of 13824 cubic feel and 216 cubic feet?

Mathematics
1 answer:
velikii [3]3 years ago
3 0

Answer: The scale factor is 4

Step-by-step explanation:

We know that the pyramids are similar. The volume of one of these pyramids is  13,824 cubic feet and the volume of the other one is 216 cubic feet. Then:

V_1=13,824ft^3\\V_2=216ft^3

By Similar solids theorem, if two similar solids have a scale factor of \frac{a}{b}, then corresponding volumes have a ratio of \frac{a^3}{b^3}

Then:

\frac{V_1}{V_2}=\frac{a^3}{b^3}

Knowing this, we can find the scale factor. This is:

\frac{13,824}{216}=\frac{a^3}{b^3}\\\\\frac{13,824}{216}=(\frac{a}{b})^3\\\\\frac{a}{b}=\sqrt[3]{\frac{13,824}{216}}\\\\scale\ factor=\frac{a}{b}=4

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