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: Find the scale factor of radii

For similar cylinders, the ratio of corresponding linear dimensions (like radius, height) is equal. First, find the ratio of the radius of cylinder A to cylinder B.
The radius of cylinder A ($r_A$) is 5.6 inches and radius of cylinder B ($r_B$) is 1.4 inches. So the scale factor $k=\frac{r_A}{r_B}=\frac{5.6}{1.4} = 4$.

Step2: Use scale factor to find height of A

Since the cylinders are similar, the ratio of heights ($h_A$ and $h_B$) is the same as the ratio of radii. So $\frac{h_A}{h_B}=k$. We know $h_B = 4$ inches and $k = 4$. Then $h_A=k\times h_B=4\times4 = 16$ inches. Also, height is a linear measurement, so the unit should be inches (not square inches, which is for area).

Answer:

16 inches (corresponding to the option "16 inches")