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.) 64: 125
c.) 16: 25
d.) 25: 16

A.) 125:64

Step-by-step explanation:

You know that:

Where is the volume of the first cylinder and is the vollume of the second cylinder.

Therefore, the ratio of the volumes of the two similar cylinders can be calculated as following:

Then:

Finaly the answer is A) 125:64

The ratio for the volumes of two similar cylinders = 125 : 64

Step-by-step explanation:

Formula:-

Volume of cylinder

Volume =πr²h

r - Radius of cylinder

h - Height of cylinder

To find the ratio of volumes of 2 cylinder

It is given that,  the ratio of heights and radii is 5:4

Let V₁ be the volume of 1st cylinder and V₂ be the volume of 2nd cylinder

V₁ = πr₁²h₁

V₂ = πr₂²h₂

V₁ /V₂ = πr₁²h₁/πr₂²h₂ = r₁²h₁/r₂²h₂

  = (5²*5)/(4²*4) = 125/64

Therefore the ratio for the volumes of two similar cylinders = 125 : 64

how is that middle school

step-by-step explanation:

-2

7 - 9 = -2

reversed:

-2 + 9 = 7