Question

find the hieght of the right circular cylinder if its curved surface area is 176cm² and radius of base is 4 cm​

Answer 1

Answer:

Height = 7cm

Step-by-step explanation:

CSA of cylinder = 2πrh

∴ 2πrh = 176

⇒ 2 x $\frac{22}{7}$ x 4 x h = 176

⇒  $\frac{22}{7}$ x 4 x h = $\frac{176}{2}$ = 88

⇒ 4 x h = $\frac{176}{2}$ = 88 x $\frac{7}{22}$ = 28

∴ h = $\frac{28}{4}$ = 7cm

Answer 2

Answer:

Diagram :

Here is the diagram of cylinder. See this diagram from website Brainly.in.

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{4\ cm}}\put(9,17.5){\sf{7\ cm}}\end{picture}$

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

Given :

• »» Curved surface area of cylinder = 176 cm².
• »» Radius of base of cylinder = 4 cm.

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

To Find :

• »» Height of cylinder

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

Using Formula :

CSA of cylinder = 2πrh

• »» CSA = Curved surface area
• »» π = 22/7
• »» r = radius
• »»h = height

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

Solution :

$\implies\footnotesize{\sf{CSA \: of \: cylinder = 2 \pi rh}}$

$\implies\footnotesize{\sf{176 = 2 \times \dfrac{22}{7} \times 4 \times h}}$

$\implies\footnotesize{\sf{176 = \dfrac{2 \times 22 \times 4}{7}\times h}}$

$\implies\footnotesize{\sf{176 = \dfrac{44 \times 4}{7}\times h}}$

$\implies\footnotesize{\sf{176 = \dfrac{176}{7}\times h}}$

$\implies\footnotesize{\sf{h = 176 \times \dfrac{7}{176}}}$

$\implies\footnotesize{\sf{h = \cancel{176} \times \dfrac{7}{\cancel{176}}}}$

$\implies\footnotesize{\sf{h =1 \times 7}}$

$\implies \footnotesize{\sf{\red{h =7 \: cm}}}$

• Hence, the height of cylinder is 7 cm.

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

Vefication :

$\implies\footnotesize{\sf{CSA \: of \: cylinder = 2 \pi rh}}$

$\implies\footnotesize{\sf{176 = 2 \times \dfrac{22}{7} \times 4 \times 7}}$

$\implies\footnotesize{\sf{176 = \dfrac{2 \times 22 \times 4 \times 7}{7}}}$

$\implies\footnotesize{\sf{176 = \dfrac{44 \times 28}{7}}}$

$\implies\footnotesize{\sf{176 = \dfrac{1232}{7}}}$

$\implies\footnotesize{\sf{176 = \cancel{\dfrac{1232}{7}}}}$

$\implies\footnotesize{\sf{176 = 176 }}$

$\implies \footnotesize{\sf{\red{LHS = RHS}}}$

• Hence Verified!

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

Learn More :

Here is some formulas related to cylinder. See this latex from website Brainly.in.

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

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