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

Answer 1

If two cylinders are similar, then all their linear measurements have equal ratios. Hence:

$\dfrac{r_A}{r_B} =\dfrac{h_A}{h_B}$.

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:

$\dfrac{5.6}{1.4} =\dfrac{h_A}{4}$.

Use the cross multiplication:

$1.4h_A=5.6\cdot 4,\\ 1.4h_A=22.4,\\ h_A=\dfrac{22.4}{1.4} =16$ in.

Answer: the height of cylinder A 16 inches.

Answer 2

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,

$\frac{R_{A}}{R_{B}}=\frac{H_{A}}{H_{B}}$

i.e. $x=\frac{5.6\times 4}{1.4}$

i.e. $x=\frac{22.4}{1.4}$

i.e. x = 16

Thus, the height of the cylinder A is 16 inches.

Hence, option C is correct.