Question

What is the similarity ratio of the smaller to the larger similar cylinders? Enter your answer as a:b.

Answer 1

The ratio of their linear dimensions is the square root of the ratio of their areas. The ratio of their areas is 1.5625. The ratio of their linear dimensions is 1.25. I guess you could write it as 5:4. oops. The smaller to the larger. That's 4:5.

Answer 2

Answer: The required similarity ratio of the smaller to the larger similar cylinder is

a : b = 4 : 5.

Step-by-step explanation: We are given to find the similarity ratio of the smaller to the larger similar cylinder.

Let S and S' be the surface area of the smaller and bigger cylinders respectively.

Then, according to the given information, we have

`S=48\pi~\textup{m}^2,\\\\S'=75\pi~\textup{m}^2.`

We know that

Similarity ratio of two cylinders is the ratio of the radii of the two cylinders and the ratio of the surface area of the two cylinders is the square of the similarity ratio.

Therefore, if a and b represents the radius of the smaller and bigger cylinder respectively, then

`(S)/(S')=(48\pi)/(75\pi)\\\\\\\Rightarrow (a^2)/(b^2)=(16)/(25)\\\\\\\Rightarrow (a^2)/(b^2)=(4^2)/(5^2)\\\\\\\Rightarrow \left((a)/(b)\right)^2=\left((4)/(5)\right)^2\\\\\\\Rightarrow (a)/(b)=(4)/(5)\\\\\Rightarrow a:b=4:5.`

Thus, the required similarity ratio of the smaller to the larger similar cylinder is

a : b = 4 : 5.