The volume of a cylindrical can is 3.08 liter. If the area of its base

1.	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» 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, $\displaystyle\colon\rarr\sf\: CSA=2\times \dfrac{22}{\cancel7}\times\cancel7 \times 20 \:cm^2\\ \\ \sf\colon\rarr \: 2\times 22\times 20 \: cm^2\\ \\ \red{\colon\dashrightarrow}\underline{\boxed{\bf{\pink{CSA=880\:cm^2}}}}$ $\\$ $\therefore\;\underline{\sf The\:CSA\: of\:the\:cylinder=\bf{880\:cm^2.}}\\$ $\\$ _____________________________

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»

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,

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

$\\$

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

$\\$

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.

_____________________________

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