If two cylinders are similar, then all their linear measurements have equal ratios. Hence:
[tex] \dfrac{r_A}{r_B} =\dfrac{h_A}{h_B} [/tex].
Since the radius of cylinder A is 5.6 inches, the radius of cylinder B is 1.4 inches and the height of cylinder B is 4 inches, you can find the height of cylinder A:
[tex] \dfrac{5.6}{1.4} =\dfrac{h_A}{4} [/tex].
Use the cross multiplication:
[tex] 1.4h_A=5.6\cdot 4,\\ 1.4h_A=22.4,\\ h_A=\dfrac{22.4}{1.4} =16 [/tex] in.
Answer: the height of cylinder A 16 inches.
Answer:
C. 16 inches is correct
Step-by-step explanation:
We are given the dimensions of the cylinders as,
Cylinder A: Radius = 5.6 inches and Height = x inches
Cylinder B: Radius = 1.4 inches and Height = 4 inches
Now, as the cylinders are similar, the ratio of the measurements will be equal.
So, we get,
[tex]\frac{R_{A}}{R_{B}}=\frac{H_{A}}{H_{B}}[/tex]
i.e. [tex]x=\frac{5.6\times 4}{1.4}[/tex]
i.e. [tex]x=\frac{22.4}{1.4}[/tex]
i.e. x = 16
Thus, the height of the cylinder A is 16 inches.
Hence, option C is correct.
