Question

two cylinders are similar. the radius of cylinder a is 5.6 inches. the radius of cylinder b is 1.4 inches. if the height of cylinder b is 4 inches, what is the height of cylinder a? 8.2 inches 8.2 square inches 16 inches 16 square inches

Explanation:

Step1: Set up proportion for similar - cylinders

For similar cylinders, the ratio of radii is equal to the ratio of heights. Let the height of cylinder A be $h_A$. The ratio of the radius of cylinder A to the radius of cylinder B is equal to the ratio of the height of cylinder A to the height of cylinder B. So, $\frac{r_A}{r_B}=\frac{h_A}{h_B}$.

Step2: Substitute the given values

We know that $r_A = 5.6$ inches, $r_B=1.4$ inches, and $h_B = 4$ inches. Substituting these values into the proportion $\frac{5.6}{1.4}=\frac{h_A}{4}$.

Step3: Solve for $h_A$

First, simplify $\frac{5.6}{1.4}=4$. Then the equation becomes $4=\frac{h_A}{4}$. Cross - multiply to get $h_A=4\times4 = 16$ inches.

Answer:

C. 16 inches