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

C) 1,500 m³

Explanation:

`k - \text{scale of similar}`

`\text{If}\ AB\sim CD\ \text{in scale}\ k,\ \text{then}\ (length_(AB))/(length_(CD))=k`

`\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ (area_A)/(area_B)=k^2`

`\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ (volume_A)/(volume_B)=k^3`

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

`(V_B)/(12)=125` multiply both sides by 12

`V_B=1500\ m^3`