Question

cylinders a and b are similar solids. the base of cylinder a has a circumference of 4π units. the base of cylinder b has an area of 9π units. the dimensions of cylinder a are multiplied by what factor to produce the corresponding dimensions of cylinder b? 4/9 2/3 3/2 9/4

Explanation:

Step1: Find radius of cylinder A

The formula for the circumference of a circle is $C = 2\pi r$. Given $C = 4\pi$, we have $4\pi=2\pi r_A$, so $r_A = 2$.

Step2: Find radius of cylinder B

The formula for the area of a circle is $A=\pi r^{2}$. Given $A = 9\pi$, we have $9\pi=\pi r_B^{2}$, so $r_B^{2}=9$ and $r_B = 3$.

Step3: Find the scale - factor

The scale - factor $k$ from cylinder A to cylinder B is given by $\frac{r_B}{r_A}$. Substituting $r_A = 2$ and $r_B = 3$, we get $k=\frac{3}{2}$.

Answer:

$\frac{3}{2}$