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:

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

3 0

2 years ago

Janine wants a necklace 45 beads long

seraphim [82]

If there are 45 beads, with a ratio of $1:4$
Then,
$\frac{45}{5}=9$
Then if $\frac{1}{4}=\frac{9}{x}$
Then $x=9*4$
Therefore, $x=36$
Meaning, there would be a ratio of 36 beads to 9 beads

4 0

3 years ago

Read 2 more answers