Question

Consider two rectangular medicine boxes labeled as B1 and B2. For box B1, theratio of the length to the width to the height is 5:2:1. For box B2, the ratio of thelength to the width to the height is 6:2:1. If the widths of the two boxes are equal,what is the ratio of the volume of B1 to the volume of B2?

Answer 1

Volume of a rectangular box is

$v=\text{lbh}$

for B1, the ratio is 5:2:1

For B2, the ratio is 6:2:1

Given,

2x=2x

x=2

thus,

the volume of B1 is

$10\times4\times2=80$

the volume of B2 is

$12\times4\times2=96$

Thus the ratio is

$\frac{80}{96}=\frac{5}{6}$