Question

If the ratio of the volumes of two cylinders of equal height is 25:36, what is the ratio of their radii?
1️⃣ 5:6
2️⃣ 6:5
3️⃣ 16:5
4️⃣ 36:2
Please give full answer in explanation​

Answer 1

Given

• Ratio of the volumes of two Cylinders = 25:36
• π = 22/7 or 3.14

Explanation:

❍ Let the Radius of Cylinders be x and Height be h and then Volumes of Cylinders be ${\sf{ V_1, V_2}}$ :

$\maltese \ {\boxed{\underline{\sf\large{ Volume_{(Cүlinder)} = πr^2h }}}}$

Where as:

• r = Radius
• h = Height

The volume of the cylinder can be given by the product of the area of base and height.

$\\ \bigstar {\underline{\pmb{\sf{ According \ to \ Question: }}}} \\ \\ \colon\implies{\sf{ \dfrac{V_1}{V_2} = \dfrac{πr^2h}{πr^2h} }} \\ \\ \\ \colon\implies{\sf{ \dfrac{25}{36} = \dfrac{ \cancel{π} \ x^2 \ \cancel{h} }{ \cancel{π} \ x^2 \ \cancel{h} } }} \\ \\ \\ \colon\implies{\sf{ \dfrac{25}{36} = \dfrac{x^2}{x^2} }} \\ \\ \\ \colon\implies{\sf{ 25x^2 = 36x^2 }} \\ \\ \\ \colon\implies{\sf{ (5x)^{ \cancel{2} } = (6x)^{ \cancel{2 } } }} \\ \\ \\ \colon\implies{\sf{ 5 \cancel{x} = 6 \cancel{x} }} \\ \\ \\ \colon\implies{\sf{ 5 = 6 }} \\ \\ \colon\implies{\boxed{\sf\red{ 5 \colon 6 }}}$

Hence,

${\underline{\sf{The \ Ratio \ of \ the \ Radius \ of \ two \ Cylinders \ will \ be \ 5:6 }}}$

Answer 2

Answer:

5:6

Step-by-step explanation:

Volume of a cylinder 1 = π$r_{1} ^{2}$$h_{1}$

Volume of a cylinder 2 = π$r_{2} ^{2}$$h_{2}$

but $h_{1} = h_{2}$

$\frac{V_{1} }{V_{2} }$  = $\frac{25}{36}$ = $\frac{\pi r_{1} ^{2} h}{\pi r_{2} ^{2} h}$ = $(\frac{r_{1} }{r_{2} } )^{2}$

Hence, $\frac{r_{1} }{r_{2} } = \sqrt{\frac{25}{36} } = \frac{5}{6}$