Question

The ratio of the radii of two right circular cylinders is 1 : 2 and the ratio of their heights is 4 : 1 . The ratio of their volumes is​

Answer 1

Given:-

• Ratio of Radius = 1 : 2
• Ratio of heights = 4 : 1

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Need to find:-

• Ratio of volumes = ?

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Solution:-

Let:

• Volume of 1st cylinder = V1
• Volume of 2nd Cylinder = V2

Volume of 1st cylinder = V1

$\rightarrow \: {v}_{1} = \pi {R1}^{2}{h}_{1}$

Volume of 2nd Cylinder = V2

$\rightarrow \: {V}_{2} = \pi {r2}^{2} {h}_{2}$

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The ratio of their volumes:-

→$\dfrac{v1}{v2} = \dfrac{\pi {r1}^{2}h1 } {\pi {r2}^{2} h2}$

→ $\dfrac{{v}_{1}}{{v}_{2}} = \dfrac{ {r1}^{2} {h}_{1}}{ {r2}^{2}{h}_{2} }$

→$\dfrac{v1}{v2} = { \dfrac{r1}{r2} }^{2} \dfrac{h1}{h2}$

→ $\dfrac{{v}_{1}}{{v}_{2}} = { \dfrac{1}{2} }^{2} \times \dfrac{4}{1}$

→ $\dfrac{v1}{v2} = \dfrac{1}{4} \times \dfrac{4}{1}$

→ $\red{\large{\boxed{\bold{ \dfrac{v1}{v2} = \dfrac{1}{1} }}}}$

The ratio of their volumes is 1:1.

Answer 2

Given :

The ratio of the radii of two right circular cylinders is 1 : 2 and the ratio of their heights is 4 : 1.

To FinD :

The ratio of their volumes.

Solution :

Analysis :

Here the formula of volume of cylinder is used. First we have to substitute the values of the radii and heights of the two cylinders in their request places. Then comparing those we can find the ratio of their volumes.

Required Formula :

Volume of cylinder = πr²h

where,

• π = 22/7
• r = radius
• h = height

Explanation :

Formula of volume of first cylinder :

$\\ :\large\boxed{\bf V_1=\pi r^2_1h_1}$

where,

• π = 22/7
• r₁ = 1
• h₁ = 4
• V₁ = Volumes of 1st cylinder

Formula of volume of second cylinder :

$\\ :\large\boxed{\bf V_2=\pi r^2_2h_2}$

where,

• π = 22/7
• r₂ = 2
• h₂ = 1
• V₂ = Volume of 2nd cylinder

Using the required formula and substituting the required values,

$\\ :\implies\normalsize\sf\dfrac{V_1}{V_2}=\dfrac{\pi r^2_1h_1}{\pi r^2_2h_2}$

$\\ :\implies\normalsize\sf\dfrac{V_1}{V_2}=\dfrac{\pi (1)^2\times4}{\pi (2)^2\times1}$

$\\ :\implies\normalsize\sf\dfrac{V_1}{V_2}=\dfrac{\cancel{\pi}(1)^2\times4}{\cancel{\pi}(2)^2\times1}$

$\\ :\implies\normalsize\sf\dfrac{V_1}{V_2}=\dfrac{1\times4}{4\times1}$

$\\ :\implies\normalsize\sf\dfrac{V_1}{V_2}=\dfrac{4}{4}$

$\\ :\implies\normalsize\sf\dfrac{V_1}{V_2}=\cancel{\dfrac{4}{4}}$

$\\ :\implies\normalsize\sf\dfrac{V_1}{V_2}=\dfrac{1}{1}$

$\\ \normalsize\therefore\boxed{\bf V_1:V_2=1:1}$

The ratio of the volume of the two cylinders is 1 : 1.