Question

What is the ratio for the volumes of two similar cylinders, given that the ratio of their heights and radii is 5:4

A)125:64
B)25:16
C)64:125
D)16:25

Answer 1

I think the answer is d

Answer 2

Answer: The correct option is (A) 125 : 64.

Step-by-step explanation: Given that the ratio of the heights and radii of two similar cylinders is 5 : 4.

We are to find the ratio for 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, r' be the radii and h, h' be the heights of the two similar cylinders.

Then, the volumes of the two cylinders will be

`V=\pi r^2h,\\\\\\V'=\pi r'^2h'.`

According to the given information, we have

`(r)/(r')=(h)/(h')=(5)/(4).`

Therefore, we get

`(V)/(V')=(\pi r^2h)/(\pi r'^2h')=\left((r)/(r')\right)^2*(h)/(h')=\left((5)/(4)\right)^2*(5)/(4)=(125)/(64)=125:64.`

Thus, the required ratio of the volumes of the two cylinders is 125 : 64.

Option (A) is CORRECT.