Question

Box A has a volurme of 12 cublic meters. Box B is similar to box A. To create Box B, Box A's dimensions were multiplied by five. What is the volume of Box B?

A) 60 m^3
B)300 m^3
C) 1,500 m^3
D) 7,500 m^3

Answer 1

Answer:

C) 1,500 m³

Step-by-step explanation:

$k - \text{scale of similar}$

$\text{If}\ AB\sim CD\ \text{in scale}\ k,\ \text{then}\ \dfrac{length_{AB}}{length_{CD}}=k$

$\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{area_A}{area_B}=k^2$

$\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{volume_A}{volume_B}=k^3$

$\text{We have}\ B\sim A\ \text{in scale}\ k=5.\ V_A=12\ m^3,\ \text{therefore}\\\\\dfrac{V_B}{V_A}=k^3\to\dfrac{V_B}{12}=5^3$

$\dfrac{V_B}{12}=125$            multiply both sides by 12

$V_B=1500\ m^3$