Question

Volume of a cylinder is 44 Cubic cm and radius is 2 cm. Find its whole surface.​

Answer 1

According to the given question,

Volume of cylinder = π × r × 2 × h

➪ .22/7×2×2×h = 44

➪ 12.57×h = 44

➪ h = 3.5 cm

Surface area of cylinder = π r² h

Surface area of cylinder = 22/7×2²×3.5

Surface area of cylinder = 44 cm²

Therefore surface area of the cylinder = 44cm²

Answer 2

Step-by-step explanation:

Correct Question:-

Volume of a cylinder is 44 Cubic cm and radius is 2 cm. Find its Total Surface Area.

Diagram:-

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

Given:-

Volume of a Cylinder=44cm$\sf {}^3$

Radius=r=2cm

To find:-

TSA of the Cylinder.

Solution:-

We know that

$\boxed{\sf Volume_{(Cylinder)}=\pi r^2h}$

$\\ \sf{:}\longrightarrow 44=\dfrac{22}{7}\times (2)^2\times h$

$\\ \sf{:}\longrightarrow 44=\dfrac{22}{7}\times 4\times h$

$\\ \sf{:}\longrightarrow h=\dfrac{44\times 7}{22\times 4}$

$\\ \sf{:}\longrightarrow h=\dfrac{308}{88}$

$\\ \bf{:}\longrightarrow h=3.5cm$

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Now,

$\\ \sf{:}\longrightarrow TSA_{(Cylinder)}=2\pi rh+2\pi r^2$

$\\ \sf{:}\longrightarrow TSA_{(Cylinder)}=2\times \dfrac{22}{7}\times 2\times 3.5+2\times \dfrac{22}{7}\times (2)^2$

$\\ \sf{:}\longrightarrow TSA_{(Cylinder)}=2\times \dfrac{22}{7}\times 2\times 3.5+2\times \dfrac{22}{7}\times (2)^2$

$\\ \sf{:}\longrightarrow TSA_{(Cylinder)}=\dfrac{2\times 22\times 2\times 3.5}{7}+\dfrac{2\times 22\times 4}{7}$

$\\ \sf{:}\longrightarrow TSA_{(Cylinder)}=\dfrac{308}{7}+\dfrac{176}{7}$

$\\ \sf{:}\longrightarrow TSA_{(Cylinder)}=\dfrac{308+176}{7}$

$\\ \sf{:}\longrightarrow TSA_{(Cylinder)}=\dfrac{484}{7}$

$\\ \sf{:}\longrightarrow TSA_{(Cylinder)}=69.1$

$\\ \sf{:}\longrightarrow TSA_{(Cylinder)}=69cm^2(Approx)$

$\sf More\:to\:know{\begin{cases}\bigstar\:\underline{\bf{Formulae\; Related\; to\: Cylinder :}}\\\\\sf {\boxed{\footnotesize\sf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\boxed{\footnotesize\sf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\boxed{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\boxed{\footnotesize\textsf{4}}} \: \:\sf Volume=\pi r^2h\end{cases}}$