Question

The ratio of the radius to the height of a cylinder is 1:2. If the curved surface srea is 176 sq.cm, what is its volume​

Answer 1

⇝Given :-

• Curved Surface Area = 176 cm²
• Ratios = 1:2

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⇝To Find :-

• Volume = ?

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⇝Solution :-

❒ We know that :

${\large{\red{\bigstar \: \: \: \: \: \: {\orange{\underbrace{\underline{\green{\bf{CSA = 2πrh}}}}}}}}}$

❒ First finding base and height :

✏Let :

Radius = 2x

Height = 1x

✏Finding :

${\large{:{\longmapsto{\bf{CSA =2πrh}}}}}$

${\large{:{\longmapsto{\bf{176=2 \times \frac{22}{7} \times 2x \times 1x}}}}}$

${\large{:{\longmapsto{\bf{176 = \frac{44}{7} \times 2x }}}}}$

${\large{:{\longmapsto{\bf{176 = \frac{88}{7}x}}}}}$

${\large{:{\longmapsto{\bf{176 \times 7 = 88x}}}}}$

${\large{:{\longmapsto{\bf{1232 = 88x}}}}}$

${\large{:{\longmapsto{\bf{x = {\cancel\frac{1232}{88} }}}}}}$

${\blue{\dashrightarrow{\red{\underline{\bf{X = 14}}}}}}$

❒ So :

Radius = 2x = 2 × 14 = 28

Height = 1x = 1 × 14 =14

❒ Now Volume :

✏We know that :

${\large{\red{\bigstar \: \: \: \: \: \: {\orange{\underbrace{\underline{\green{\bf{Volume = πr²h}}}}}}}}}$

❒ Solving Starts :

${\large{:{\longmapsto{\bf{volume=πr²h}}}}}$

${\large{:{\longmapsto{\bf{volume= \frac{22}{7} \times ({28})^{2} \times 14 }}}}}$

${\large{:{\longmapsto{\bf{volume= \frac{22}{7} \times 784\times 14 }}}}}$

${\large{:{\longmapsto{\bf{volume={\cancel \frac{241472}{7} }}}}}}$

${\large{\red{:{\twoheadrightarrow{\purple{\underline{\boxed{\bf{Volume =34496 {cm}^{3} }}}}}}}}}$

❒ Hence :

${\large{\purple{\underline{\red{\underline{\pink{\pmb{\mathfrak{Volume = 34496cm³}}}}}}}}}</p><p>$

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Answer 2

$\large \dag$ Question :-

The ratio of the radius to the height of a cylinder is 1 : 2. If the curved surface area is 176 cm², what is its volume ?

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{Volume  \: of \:  Cylinder  \: is \: 88\sqrt{14} \:  cm^3}} }$

$\large \dag$ Step by step Explanation :-

We Know that volume of Cylinder is :

$\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{ V = \pmb\pi {r}^{2} h }}}$

And CSA of cylinder is :

$\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{  CSA = 2 \pmb\pi rh}}}$

Where,

• r = Radius of base of Cylinder

• h = Height of Cylinder

• $\sf \large\pi = \dfrac{22}{7}$

❒ Finding Radius and Height :-

Here in the Question we are given that :

✧ The ratio of the radius to the height of a cylinder is 1 : 2

Therefore Let us Assume that,

• $\small \text{Radius of Cylinder = \large r = x }$

• $\small\text{Height of Cylinder = \large h = 2x}$

✧ As the curved surface area is 176 cm²

Using Formula of CSA of Cylinder :

$:\longmapsto \rm 2 \times \frac{22}{7} \times x \times 2x = 176$

$:\longmapsto \rm \frac{88}{7} {x}^{2} = 176$

$:\longmapsto \rm {x}^{2} = 176 \div \frac{88}{7}$

$:\longmapsto \rm {x}^{2} = 176 \times \frac{7}{88}$

$:\longmapsto \rm {x}^{2} = \frac{1232}{22}$

$:\longmapsto \rm {x}^{2} = 14$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = \sqrt{14} } }}}$

Therefore,

$\blue\dashrightarrow\underline{\underline{\sf  \pink{Radius  \: of \:  Cylinder  =\sqrt{14}\: cm}} }$

$\blue\dashrightarrow\underline{\underline{\sf  \pink{Height  \: of \:  Cylinder  =2\sqrt{14}\: cm}} }$

❒ Finding Volume of Cylinder :-

Using Formula for Volume :

$:\longmapsto \rm Volume = \frac{22}{7} \times {( \sqrt{14} \: )}^{2} \times 2 \sqrt{14}$

$:\longmapsto \rm Volume = \frac{22}{7} \times 14 \times 2 \sqrt{14}$

$\purple{ :\longmapsto  \underline {\boxed{{\bf Volume = 88 \sqrt{14} \: cm {}^{3} } }}}$

Therefore,

$\underline{\pink{\underline{\frak{\pmb{\text Volume  \: of \:  C \text ylinder  \: is \: 88\sqrt{14} \:  cm^3 }}}}}$