Question

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Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

$\tt Given \begin{cases} \sf{Ratio \: between \: radius \: and \: height \: is \: 2 : 3 } \\ \sf{Volume \: of \: cylinder \: is \: 12936 \: cm^3.}\end{cases}$

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To Find :

$\hookrightarrow \sf{Radius \: of \: the \: base \: of \: cylinder }$

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Solution :

Let the radius be 2x.

So, height will be 3x.

Now,

We know the formula of the volume of cylinder,

$\large{\star{\underline{\boxed{\sf{Volume = \pi r^2 h}}}}}$

$\sf{ \rightarrow \: 12936 = \frac{22}{7} \times ( {2x)}^{2} \times 3x } \\ \\ \sf{\rightarrow12936 = \frac{22} \: {7} \times 2x \times 2x \times 3x } \\ \\ \sf{ \rightarrow \: \cancel{12936} \times \frac{7}{ \cancel{22}} = \: 12 {x}^{3}} \\ \\ \sf{\rightarrow \: 588 \times 7 = 12 {x}^{3} } \\ \\ \sf{\rightarrow \: 4116 = 12 {x}^{3} } \\ \\ \sf{\rightarrow \: \frac{ \cancel{4116}}{ \cancel{12}} = {x}^{3} } \\ \\ \sf{\rightarrow \: 343 = {x}^{3} } \\ \\ \sf{\rightarrow \: {7}^{ \cancel3} = {x}^{ \cancel3} } \\ \\ \sf{\rightarrow \: x = 7 \: cm}$

$\large{\star{\underline{\boxed{\sf{x = 7 \: cm}}}}}$

So, radius = 2x = 2(7) = 14 cm

Height = 3x = 3(7) = 21 cm

$\rule{200}{2}$

Verification :

$\sf{\rightarrow 12936= \frac{22}{\cancel7} (14)^2 \times \cancel{21} } \\ \\ \sf{\rightarrow 12936 = 22 \times 196 \times 3} \\ \\ \sf{\rightarrow 12936 = 22 \times 588}\\ \\ \sf{12936 \: cm^3= 12936 \: cm^3} \\ \\ \bf{Hence \: Proved}$

$\rule{200}{2}$

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Answer 2

Solution:

Given:

➜ The ratio between the radius of the base and the height of the cylinder is 2 : 3. If the volume of the cylinder is 12936 cm³, find the radius of the base of the cylinder.

Find:

➜ Find the radius of the base of the cylinder.

According to the given question:

➜ 2:3 = height of the cylinder.

➜ 12936 cm³ = volume of the cylinder.

Calculations:

➜ Let us assume "2M" as radius and "3M" as height.

Formula:

➜ Volume of cylinder => πr² h.

Step-by-step:

➜ 12936 = 22/7 × (2M) ² × 3M

➜ 12936 = 22/7 × 2M × 2M × 3M

➜ 12936 × 7/22 = 12M³

➜ 588 × 7 = 12M³

➜ 4116 = 12M³

➜ 4116/12 = M³

➜ 343 = M³

➜ M = 7 cm

➜ Radius = 2M = 2 × 7 = 14

➜ Height = 3M = 3 × 7 = 21

Verification:

➜ 12936 = 22/7 × 14² × 21

➜ 12936 = 22 × 196 × 3

➜ 12936 = 22 × 588

➜ 12936 cm² = 12936 cm²

Therefore Proved!!

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