Question

The volume of a cylindrical can is 3.08 liter. If the area of its base is 154 sq.cm. Find its curved surface area.
Please answer with a picture of clear explanation.

Answer 1

Answer:

$\frak{Given}\begin{cases}\sf{Volume\:of\:Cylinder=\bf{3.08\:litre.}}\\\sf{Area\:of\:Base=\bf{154\:sq\:cm.}}\end{cases}$

$\underline{\bf{\bigstar\:To\:Find:-}}$

• The Curved Surface Area (CSA) .

$\underbrace{\underline{\bf{\bigstar\:Required\:Solution:-}}}$

» We are given with the area of base of cylinder, which is nothing else but the area of a circle, using this we would find the radius of the cylinder.

» Then, using the radius and the given volume, we would find the height of the cylinder.

» After finding the radius and height, using the formula, we would find the Curved surface Area of the cylinder.

◐ Finding the radius of the cylinder ◑

We have -

• Area of base = 154 cm²

We know:

$\odot\;\boxed{\sf Area_{\:circle}=\pi r^2}$

So,

$\displaystyle \colon \rarr \sf \: \cancel{154 }\: {cm}^{2} = \dfrac{ \cancel{22}}{7} \times {r}^{2} \\ \\ \displaystyle\colon \sf \rarr \: 7 \times 7 \: {cm}^{2} = {r}^{2} \\ \\ \colon \rarr \sf \: r = \sqrt{7 \times 7 \: {cm}^{2} } \\ \\ \red{\colon \dashrightarrow} \boxed{ \frak{ \green{r = 7 \: cm}}}$

◐ Finding the height of the cylinder ◑

We have :

• Radius = 7cm
• Volume = 3.08 litre = 3.08×1000 cm³ = 3080 cm³

We know :

$\odot\;\boxed{\sf Volume_{\:cylinder}=\pi r^2h}$

So,

$\displaystyle \colon \rarr \sf \: \cancel{3080} \: {cm}^{ 3} = \frac{ \cancel{22}} {7} \times {(7 \: cm)}^{2} \times h \quad\\ \\ \displaystyle \colon \rarr \sf \: \cancel{ 140 }\: {cm}^{3} = \frac{1}{ \cancel7} \times \cancel7 \: cm \times \cancel7 \: cm \times h \\ \\ \colon \sf\rarr \: 20 \: \cancel {cm}^{3} = h \: \cancel {cm}^{2} \\ \\ \red{\colon \dashrightarrow} \boxed{ \frak{ \purple{h = 20 \: cm}}}$

◐ Finding CSA of the cylinder ◑

We have :

• Radius = 7 cm
• Height = 20 cm

We know :

$\odot\;\boxed{\sf CSA_{\:cylinder}=2\pi rh}$

So,

$\displaystyle\colon\rarr\sf\: CSA=2\times \dfrac{22}{\cancel7}\times\cancel7 \times 20 \:cm^2\\ \\ \sf\colon\rarr \: 2\times 22\times 20 \: cm^2\\ \\ \red{\colon\dashrightarrow}\underline{\boxed{\bf{\pink{CSA=880\:cm^2}}}}$

$\therefore\;\underline{\sf The\:CSA\: of\:the\:cylinder=\bf{880\:cm^2.}}$

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Answer 2

Answer:

$\red{\begin{gathered}\frak{Given}\begin{cases}\sf{Volume\:of\:Cylinder=\bf{3.08\:litre.}}\\\sf{Area\:of\:Base=\bf{154\:sq\:cm.}}\end{cases}\end{gathered}}$

$\pink{\begin{gathered} \\ \end{gathered}\underline{\bf{\bigstar\:To\:Find:-}}}$

The Curved Surface Area (CSA) .

$\green{\begin{gathered} \\ \end{gathered}\underbrace{\underline{\bf{\bigstar\:Required\:Solution:-}}}}$

» We are given with the area of base of cylinder, which is nothing else but the area of a circle, using this we would find the radius of the cylinder.

» Then, using the radius and the given volume, we would find the height of the cylinder.

» After finding the radius and height, using the formula, we would find the Curved surface Area of the cylinder.

\begin{gathered} \\ \end{gathered}

◐ Finding the radius of the cylinder ◑

We have -

Area of base = 154 cm²

We know:

${\odot\;\boxed{\sf Area_{\:circle}=\pi r^2}}$

So,

$\begin{gathered} \displaystyle \colon \rarr \sf \: \cancel{154 }\: {cm}^{2} = \dfrac{ \cancel{22}}{7} \times {r}^{2} \\ \\ \displaystyle\colon \sf \rarr \: 7 \times 7 \: {cm}^{2} = {r}^{2} \\ \\ \colon \rarr \sf \: r = \sqrt{7 \times 7 \: {cm}^{2} } \\ \\ \red{\colon \dashrightarrow} \boxed{ \frak{ \green{r = 7 \: cm}}}\end{gathered}$

◐ Finding the height of the cylinder ◑

We have :

◐ Finding the height of the cylinder

We have :Radius = 7cmVolume = 3.08 litre = 3.08×1000 cm³ = 3080 cm³We know :

$\blue{\odot\;\boxed{\sf Volume_{\:cylinder}=\pi r^2h}}$

So,

$\begin{gathered} \displaystyle \colon \rarr \sf \: \cancel{3080} \: {cm}^{ 3} = \frac{ \cancel{22}} {7} \times {(7 \: cm)}^{2} \times h \quad\\ \\ \displaystyle \colon \rarr \sf \: \cancel{ 140 }\: {cm}^{3} = \frac{1}{ \cancel7} \times \cancel7 \: cm \times \cancel7 \: cm \times h \\ \\ \colon \sf\rarr \: 20 \: \cancel {cm}^{3} = h \: \cancel {cm}^{2} \\ \\ \red{\colon \dashrightarrow} \boxed{ \frak{ \purple{h = 20 \: cm}}}\end{gathered}\begin{gathered} \\ \end{gathered}$

◐ Finding CSA of the cylinder

We have :

Radius = 7 cm

Height = 20 cm

We know :

$\orange{\odot\;\boxed{\sf CSA_{\:cylinder}=2\pi rh}}$

So,

$\begin{gathered}\displaystyle\colon\rarr\sf\: CSA=2\times \dfrac{22}{\cancel7}\times\cancel7 \times 20 \:cm^2\\ \\ \sf\colon\rarr \: 2\times 22\times 20 \: cm^2\\ \\ \red{\colon\dashrightarrow}\underline{\boxed{\bf{\pink{CSA=880\:cm^2}}}}\end{gathered}</p><p>\begin{gathered} \\ \end{gathered}\begin{gathered}\therefore\;\underline{\sf The\:CSA\:of\:the\:cylinder=\bf{880\:cm^2.}}\\\end{gathered}$

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