Question

Two cylinders have same base radius r. If their heights are 5 cm and 15 cm. What is the ratio of their volumes?

DONT SAY WRONG ANSWER

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question}}}$

Here the concept of Volume of Cylinder has been used. We are given that two cylinders have same radius of their base. This means the variable component is only their height. Firstly using the formula os Volume of Cylinder, we can calculate the volume of both cylinders separately and then find their ratio.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{\pink{Volume\;of\;Cylinder\;=\;\bf{\pi r^{2}h}}}}$

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★ Solution :-

Given,

» Radius of both cylinders = r

» Height of two cylinders = 5 cm and 15 cm

• Let the smaller cylinder be C₁

• Let the bigger cylinder be C₂

• For Smaller Cylinder ::

→ Radius = r

→ Height = h₁ = 5 cm

• For Bigger Cylinder ::

→ Radius = r

→ Height = h₂ = 15 cm

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~ For Volume of both the Cylinders ::

We know that,

$\\\;\sf{Volume\;of\;Cylinder\;=\;\bf{\pi r^{2}h}}$

• For cylinder C₁ :-

$\\\;\sf{:\rightarrow\;\;Volume\;of\;Cylinder,\;C_{1}\;=\;\bf{\pi r^{2}h_{1}}}$

By applying values, we get

$\\\;\sf{:\rightarrow\;\;Volume\;of\;Cylinder,\;C_{1}\;=\;\bf{\orange{\pi\:\times\:r^{2}\:\times\:5}}}$

• For cylinder C₂ :-

$\\\;\sf{:\rightarrow\;\;Volume\;of\;Cylinder,\;C_{2}\;=\;\bf{\pi r^{2}h_{2}}}$

By applying values, we get

$\\\;\sf{:\rightarrow\;\;Volume\;of\;Cylinder,\;C_{1}\;=\;\bf{\green{\pi\:\times\:r^{2}\:\times\:15}}}$

*Note :: Here we shall leave π as it is only. We no need to apply its values since it is going to be cancelled in last step.

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~ For the Ratio of Volume of Two Cylinders ::

The ratio of volume of two cylinders is given as,

$\\\;\bf{\Longrightarrow\;\;Ratio\;of\;Volume\;of\;Cylinders\;=\;\bf{\dfrac{\orange{C_{1}}}{\green{C_{2}}}}}$

Now by applying values, we get

$\\\;\sf{\Longrightarrow\;\;Ratio\;of\;Volume\;of\;Cylinders\;=\;\bf{\red{\dfrac{\pi\:\times\:r^{2}\:\times\:5}{\pi\:\times\:r^{2}\:\times\:15}}}}$

Now cancelling π, we get

$\\\;\sf{\Longrightarrow\;\;Ratio\;of\;Volume\;of\;Cylinders\;=\;\bf{\dfrac{r^{2}\:\times\:5}{r^{2}\:\times\:15}}}$

Cancelling r², we get

$\\\;\sf{\Longrightarrow\;\;Ratio\;of\;Volume\;of\;Cylinders\;=\;\bf{\dfrac{5}{15}}}$

Now converting this fraction into simplest form by dividing numerator and denominator by 5, we get

$\\\;\sf{\Longrightarrow\;\;Ratio\;of\;Volume\;of\;Cylinders\;=\;\bf{\dfrac{1}{3}}}$

This can be written as,

$\\\;\sf{\Longrightarrow\;\;\dfrac{C_{1}}{C_{2}}\;=\;\bf{\blue{\dfrac{1}{3}}}}$

Using ratio form, we can write it as

$\\\;\sf{\Longrightarrow\;\;C_{1}\;:\;{C_{2}\;=\;\bf{\blue{1\;:\;3}}}}$

This is the required answer.

$\\\;\underline{\boxed{\tt{Ratio\;\:of\;\:Volume\;=\;\bf{\purple{1\;:\;3}}}}}$

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★ More to know :-

$\\\;\sf{\leadsto\;\;CSA\;of\;Cylinder\;=\;2\pi rh}$

$\\\;\sf{\leadsto\;\;TSA\;of\;Cylinder\;=\;2\pi rh\;+\;2\pi r^{2}}$

• Cylinder is a three - dimensional solid which is in a rod like structure which has two bases and the radius is uniform.

Answer 2

Answer:

$\huge \mid \colorbox{aqua}{Answer} \mid$

Here the concept of Volume of Cylinder has been used. We are given that two cylinders have same radius of their base. This means the variable component is only their height. Firstly using the formula os Volume of Cylinder, we can calculate the volume of both cylinders separately and then find their ratio.

★ Formula Used :-

$\huge \fbox \pink{VolumeofCylinder=πr²h}$

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➪ SOLUTION :

Given,

Given,

» Radius of both cylinders = r

» Height of two cylinders = 5 cm and 15 cm

Let the smaller cylinder be C₁

Let the bigger cylinder be C₂

• For Smaller Cylinder ::

→ Radius = r

→ Height = h₁ = 5 cm

• For Bigger Cylinder ::

→ Radius = r

→ Height = h₂ = 15 cm

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

~ For Volume of both the Cylinders ::

We know that,

$\mathcal \colorbox{yellow}{Volume Of Cylinder}$ =πr²h

• For cylinder C₁ :-

By applying values, we get

$\mathcal \colorbox{yellow}{Volume Of Cylinder}$