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.) 64:125
C.) 16:25
D.) 25:16

Answer 1

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

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

Answer 2

Answer: A.) 125:64

Explanation:

You know that:

`(V_1)/(V_2)=(5)/(4)`

Where
`V_1=h_1r_1^(2)\pi` is the volume of the first cylinder and
`V_2=h_1r_2^(2)\pi` is the vollume of the second cylinder.

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

`V_2 = \pi(r_2)^2h_2`

`(r_2)/(r_1) = (5)/(4)\\\\\\r_2 = (5)/(4)r_1`

`(V_1)/(V_2)=(5)/(4)`

`h_2 = (5)/(4)h_1`

Then:

`(V_2)/(V_1) = (\pi((5)/(4)r_1)^2((5)/(4)h_1))/(\pi(r_1)^2h_1)\\\\(V_2)/(V_1) = ((5)/(4))^3\\\\(V_2)/(V_1) = (125)/(64)`

Finaly the answer is A) 125:64