Question

the large can is 4 inches tall and the small can is 2.5 inches tall, if the radius of the large can is 2.4 inches what is the radius on the small

Answer 1

If these two cans have geometrically similar (their measurements are proportional), then we can take the ratio of the radius and height:
small can height / large can height = small can radius / large can radius
2.5 / 4 = x / 2.4
x = 1.5 inches
Therefore the radius of the small can is 1.5 inches.

Answer 2

$\dfrac{\text{large can height}}{\text{small can height}} = \dfrac{\text{large can radius}}{\text{small can radius}}$

Substitute the known values into the variables:

$\dfrac{4}{2.5} = \dfrac{2.4}{\text{small can radius}}$

$\text{small can radius} = \dfrac{2.4 \times 2.5}{4}$

$\text{small can radius} = 1.5 \text{ inches}$