Question

Two similar cylinders have a scale factor of (1.6/3). Find the ratio of their volumes.

Answer 1

Answer:  The ratio of the volumes of the two cylinders is 512 : 3375.

Step-by-step explanation:  Given that two similar cylinders have a scale factor of $\dfrac{1.6}{3}.$

We are to find the ratio of the volumes of the two cylinders.

We know that

the volume of a cylinder with radius r units and height h units is given by

$V=\pi r^2h.$

Let r and R be the radii and h and H be the heights of the two cylinders.

Then, we must have

$\dfrac{R}{r}=\dfrac{1.6}{3}=\dfrac{16}{30}=\dfrac{8}{15}\\\\\Rightarrow R=\dfrac{8}{15}r.$

And, similarly,

$H=\dfrac{8}{15}h.$

Therefore, the volume of the first cylinder will be

$V_1=\pi r^2h$

and volume of the second cylinder will be

$V_2=\pi R^2H=\pi\times\left(\dfrac{8}{15}r\right)^2\times\left(\dfrac{8}{15}h\right)=\dfrac{512}{3375}\pi r^2h.$

Thus, the required ratio of the volumes of the two cylinders is given by

$\dfrac{V_2}{V_1}=\dfrac{\frac{512}{3375}\pi r^2h}{\pi r^2h}=\dfrac{512}{3375}=512:3375.$

The ratio of the volumes of the two cylinders is 512 : 3375.

Answer 2

Volume of cylinders = pi x r^2 x height

Simplifying the ratio:
1.6/3 = 16 / 30 (multiply and divide by 10 to remove the decimal)

Volume Ratio = 512:27