Question

the ratio of base radius of two cylinders is 1:2 and the volume ratio is 5:12 find the ratio of the heights of cylinders
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Answer 1

$\bf\underline{\underline{\green{SOLUTION:-}}}$

Question

• The ratio of base radius of two cylinders is 1:2 and the volume ratio is 5:12 find the ratio of the heights of cylinders?

Answer

• Ratio of height = 5:3

Given

• Ratio of base Radius of Two Cylinders = 1:2
• Volume ratio = 5:12

To Calculate

• Ratio of height of Cylinder?

Step By Step Explanation

Let base Radius of First Cylinder r1 = 1

Let base Radius of Second Cylinder r2 = 2

Volume of First Cylinder V1 = 5

Volume of Second Cylinder V2 = 12

$= \frac{v1}{v2} = \frac{\pi \: r1 ^{2}h1 }{\pi \: r1 ^{2} h2}$

⇝ 5/12 = (1/2)²×h1/h2

⇝ 5/12 = 1/4 ×h1/h2

⇝ h1/h2 = 5/12×4/1

⇝ h1/h2 = 20/12

⇝ h1/h2 = 5/3

$\bf\underline{\underline{\green{HENCE:-}}}$

• Ratio of height =5:3

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Answer 2

Question:

The ratio of base radius of two cylinders is 1:2 and the volume ratio is 5:12 find the ratio of the heights of cylinders?

Answer:

Ratio of height = 5:3

Given:

$\green{\tt:\implies \: Ratio \: of \: base \: Radius \: of \: Two \: Cylinders \: = \: 1:2 }$

$\blue{\tt:\implies \: Volume \: ratio = 5:12 }$

To find:

$\red{\tt\: Ratio \: of \: height \: of \: Cylinder? }$

so:

base Radius of First Cylinder r1 = 1

base Radius of Second Cylinder r2 = 2

Volume of First Cylinder V1 = 5

Volume of Second Cylinder V2 = 12

formula:

$\implies \sf \frac{V1}{V1} = \frac{\pi \: r1^2h1 }{ \pi \: r1^2h2}$

hence,

$\implies \sf \: \frac{5}{12} = ( \frac{1}{2} ^{2}) \times \frac{h1}{h2}$

$\implies \sf \: \frac{5}{12} = ( \frac{1}{4} ) \times \frac{h1}{h2}$

$\implies \sf \: \frac{h1}{h2} = \frac{5}{12} \times \frac{4}{1}$

$\implies \sf \: \frac{h1}{h2} = \frac{20}{12}$

$\implies \sf \frac{h1}{h2} = \frac{5}{3}$

∴ ratio of the heights of cylinders = 5:3