Question

7. Calculate the volume of cylinder of radius 1.4 m, curved surface area being 17.6 m2
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Answer 1

Answer:

The volume of the cylinder is 12.32 m³.

Step-by-step-explanation:

We have given that,

Radius of a cylinder = 1.4 m

Curved surface area of cylinder = 17.6 m²

We have to find the volume of the cylinder.

Now, we know that,

Curved surface area of cylinder = 2 π r h

⇒ 17.6 = 2 * ( 22 / 7 ) * 1.4 * h

⇒ ( 17.6 * 7 ) / ( 2 * 22 * 1.4 ) = h

⇒ h = ( 17.6 * 7 ) / ( 2 * 22 * 1.4 )

⇒ h = ( 17.6 * 70 ) / ( 2 * 22 * 14 )

⇒ h = ( 17.6 * 70 ÷ 14 ) / ( 2 * 22 )

⇒ h = ( 17.6 * 5 ) / ( 2 * 22 )

⇒ h = ( 176 * 5 ) / ( 20 * 22 )

⇒ h = 176 ÷ 22 * 5 / 20

⇒ h = 8 * 5 / 20

⇒ h = 40 ÷ 20

⇒ h = 2 m

Now, we know that,

Volume of cylinder = π r² h

⇒ Volume of cylinder = ( 22 / 7 ) * ( 1.4 )² * 2

⇒ Volume of cylinder = ( 22 / 7 ) * 1.4 * 1.4 * 2

⇒ Volume of cylinder = 22 * 1.4 ÷ 7 * 1.4 * 2

⇒ Volume of cylinder = 22 * 0.2 * 1.4 * 2

⇒ Volume of cylinder = 4.4 * 1.4 * 2

⇒ Volume of cylinder = 6.16 * 2

⇒ Volume of cylinder = 12.32 m³

∴ The volume of the cylinder is 12.32 m³.

Answer 2

${\bold{\sf{\underline{Understanding \: the \: question}}}}$

✰ This question says that there is a cylinder given it's radius is 1.4 m , it's curved surface area is 17.6 m² Afterthat this question ask us to find the volume of cylinder.

${\bold{\sf{\underline{Given \: that}}}}$

✠ Curved surface area of cylinder = 17.6 m²

✠ Radius of cylinder = 1.4 m

${\bold{\sf{\underline{To \: find}}}}$

✠ Volume of cylinder.

${\bold{\sf{\underline{Solution}}}}$

✠ Volume of cylinder = 12.32 m³

${\bold{\sf{\underline{Using \: concepts}}}}$

✠ Volume of cylinder formula.

✠ C.S.A of cylinder formula.

${\bold{\sf{\underline{Using \: formulas}}}}$

✠ Volume of cylinder = πr²h

✠ C.S.A of cylinder = 2πrh

${\bold{\sf{\underline{These \: also \: denote \: or \: means}}}}$

✠ C.S.A denotes Curved surface area.

✠ r denotes Radius

✠ h denotes Height

✠ π is pronounced as pi

✠ The value of π is ${\bold{\sf{\dfrac{22}{7}}}}$

${\bold{\sf{\underline{Some \: procedure}}}}$

✰ To solve this problem firstly we have to use the formula of CSA of cylinder afterthat putting the values we get value of h. Now we have to use the formula of Volume of cylinder afterthat putting the values we get Volume of cylinder as 12.32 m³ and this is our final result!

${\bold{\sf{\underline{Full \: solution}}}}$

✰ Finding CSA of cylinder.

↦ CSA = 2πrh

↦ 17.6 = 2 × 22/7 × 1.4 × h

↦ 17.6 = 22/7 × 2.8 × h

↦ 17.6 = 22/7 × 28/10 × h

↦ 17.6 = 11/7 × 28/5 × h

↦ 17.6 = 308/35 × h

↦ 176/10 = 308/35 × h

↦ 176/10 × 35/308 = h

↦ 88/5 × 35/308 = h

↦ 44/5 × 35/154 = h

↦ 44 × 7/154 = h

↦ 22 × 7/77 = h

↦ 22 × 1/11 = h

↦ 22/11 = h

↦ 2 = h

↦ h = 2

• Therefore, the value of h is 2 m

✰ Finding volume of cylinder.

↦ Volume = πr²h

↦ Volume = 22/7 × (1.4)² × 2

↦ Volume = 22/7 × 1.4 × 1.4 × 2

↦ Volume = 22/7 × 1.96 × 2

↦ Volume = 22/7 × 3.92

↦ Volume = 22/7 × 392/100

↦ Volume = 11/7 × 392/50

↦ Volume = 11/1 × 56/50

↦ Volume = 11/1 × 28/25

↦ Volume = 308/25

↦ Volume = 12.32 m³

• Therefore volume of cylinder is 12.32 m³

${\large{\bold{\sf{\underline{Knowledge \: booster}}}}}$

Diagram of cylinder.

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{r}}\put(9,17.5){\sf{h}}\end{picture}$

Formulas related to Surface area and volume of some shapes.

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

Formulas related to cylinder.

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$

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Holh...! Please see this answer from web or chrome guys because I give a diagram pic and some formulas but they are not shown in app that's why I request you to see this answer from chrome. See it from here please =

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