Calculate the volume of cylinder of radius 1.4 meter ,curved surface area being 17.6 meter square
Answers
Answer:
12.32m³
Step-by-step explanation:
Given----> Radius of cylinder = 1.4 m and curved surface area is 17.6 m²
To find----> Volume of cylinder
Solution----> We know that ,
Curved surface area of cylinder = 2 π r h
Volume of cylinder = π r² h
ATQ,
Radius of cylinder = 1.4 m
Curved surface area = 17.6 m²
=> 2 π r h = 17.6
=> 2 × ( 22 / 7 ) × 1.4 × h = 17.6
=> 2 × 22 × 0.2 × h = 17.6
=> 8.8 h = 17.6
=> h = 17.6 / 8.8
=> h = 2 m
Volume of cylinder = π r² h
= ( 22 / 7 ) × ( 1.4 )² × 2
= ( 22 / 7 ) × 1.96 × 2
= 22 × .28 × 2
= 12.32 m³
#Answerwithquality
#BAL
Step-by-step explanation:
{\bold{\sf{\underline{Understanding \: the \: question}}}}
Understandingthequestion
✰ 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}}}}
Giventhat
✠ Curved surface area of cylinder = 17.6 m²
✠ Radius of cylinder = 1.4 m
{\bold{\sf{\underline{To \: find}}}}
Tofind
✠ Volume of cylinder.
{\bold{\sf{\underline{Solution}}}}
Solution
✠ Volume of cylinder = 12.32 m³
{\bold{\sf{\underline{Using \: concepts}}}}
Usingconcepts
✠ Volume of cylinder formula.
✠ C.S.A of cylinder formula.
{\bold{\sf{\underline{Using \: formulas}}}}
Usingformulas
✠ Volume of cylinder = πr²h
✠ C.S.A of cylinder = 2πrh
{\bold{\sf{\underline{These \: also \: denote \: or \: means}}}}
Thesealsodenoteormeans
✠ 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}}}}
7
22
{\bold{\sf{\underline{Some \: procedure}}}}
Someprocedure
✰ 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}}}}
Fullsolution
✰ 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}}}}}
Knowledgebooster
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{gathered}\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}\end{gathered}
Formulas related to cylinder.
\begin{gathered}\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}}\end{gathered}
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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 =
https://brainly.in/question/31864350