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[tex]\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}[/tex]
[tex]\tt Given \begin{cases} \sf{Ratio \: between \: radius \: and \: height \: is \: 2 : 3 } \\ \sf{Volume \: of \: cylinder \: is \: 12936 \: cm^3.}\end{cases}[/tex]
_____________________________
To Find :
[tex] \hookrightarrow \sf{Radius \: of \: the \: base \: of \: cylinder }[/tex]
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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,
[tex]\large{\star{\underline{\boxed{\sf{Volume = \pi r^2 h}}}}}[/tex]
[tex] \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}[/tex]
[tex]\large{\star{\underline{\boxed{\sf{x = 7 \: cm}}}}}[/tex]
So, radius = 2x = 2(7) = 14 cm
Height = 3x = 3(7) = 21 cm
[tex]\rule{200}{2}[/tex]
Verification :
[tex]\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}[/tex]
[tex]\rule{200}{2}[/tex]
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#BAL
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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#BAL