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

Answer 1

Given:

If the ratio of the volumes of two cylinders of equal height is 25:36

To find:

What is the ratio of their radii?

Solution:

We know,

$\boxed{\bold{Volume\:of\:a\:cylinder = \pi r^2 h}}$

Let,

"r₁" & "r₂" → be the radii of the two cylinders

"h₁" & "h₂" → be the heights of the two cylinders

"V₁" & "V₂" → be the volumes of the two cylinders

We have,

$\frac{V_1}{V_2} = \frac{25}{36}$

$\implies \frac{\pi \:r_1^2\: h_1}{\pi \:r_2^2\: h_2} = \frac{25}{36}$

$\implies \frac{\:r_1^2\: h_1}{ \:r_2^2\: h_2} = \frac{25}{36}$

∵ h₁ = h₂ (given)

$\implies \frac{\:r_1^2}{ \:r_2^2} = \frac{25}{36}$

$\implies \frac{\:r_1}{ \:r_2} = \sqrt{\frac{25}{36}}$

$\implies \frac{\:r_1}{ \:r_2} = \sqrt{\frac{5^2}{6^2}}$

$\implies \bold{\frac{\:r_1}{ \:r_2} = \frac{5}{6}}$

Thus, the ratio of the radii of the cylinders is → 5:6.

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