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

Answer: A.) 125:64

Step-by-step explanation:

You know that:

$\frac{V_1}{V_2}=\frac{5}{4}$

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:

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

$\frac{r_2}{r_1} = \frac{5}{4}\\\\\\r_2 = \frac{5}{4}r_1$

$\frac{V_1}{V_2}=\frac{5}{4}$

$h_2 = \frac{5}{4}h_1$

Then:

$\frac{V_2}{V_1} = \frac{\pi(\frac{5}{4}r_1)^2(\frac{5}{4}h_1)}{\pi(r_1)^2h_1}\\\\\frac{V_2}{V_1} = (\frac{5}{4})^3\\\\\frac{V_2}{V_1} = \frac{125}{64}$

Finaly the answer is A) 125:64

Answer 2

Answer:

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