Question

Find the total surface area of a hellow cylinder open at both ends, if it's length is 28 cm, external radius is 7 cm and thickness is 1 cm.​

Answer 1

Answer:

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Explanation:

Answer:

Length of the cylinder = 28 cm

External radius = 7cm

Thickness = 1 cm

Total Surface Area = ?

Diagram

\setlength{\unitlength}{1.4cm} \thicklines \begin{picture}(2,0)\qbezier(0,0)(0,0)(0,2.5)\qbezier(2,0)(2,0)(2,2.5)\qbezier(0,0)(1,1)(2,0)\qbezier(0,0)( 1, - 1)(2,0) \put(1,1){\line(0,1){1}}\put(1,1){\line(0, - 1){1}}\put(0.2,1){ $\sf 28 \: cm$}\put(1.1,0.1){ $\sf 6 \: cm$}\put(1,0){\line(1,0){1}}\qbezier(0,2.5)(1,1.5)(2,2.5)\qbezier(0,2.5)(1, 3.5)(2,2.5)\end{picture}

\displaystyle\sf \underline{\bigstar\:\textsf{According to the given Question :}}

★According to the given Question :

We shall first find the radius of the cylinder which will be equal to the Difference Between the external and the internal radius.

\begin{gathered}\displaystyle\sf :\implies Radius = Outer \ Radius - Inner \ radius\\\end{gathered}

:⟹Radius=Outer Radius−Inner radius

Thickness = Inner radius

Inner Radius = 1 cm

Outer radius = 7 cm

\begin{gathered}\\\displaystyle\sf :\implies Radius = 7-1\\\\\end{gathered}

:⟹Radius=7−1

\displaystyle:\implies\textsf{Radius = \textbf{6 cm}}:⟹Radius = 6 cm

\displaystyle\sf \underline{\bigstar\:\textsf{TSA of the cylinder :}}

★TSA of the cylinder :

\begin{gathered}\displaystyle\sf \dashrightarrow TSA = 2\pi r(h+r)\\\\\end{gathered}

⇢TSA=2πr(h+r)

\begin{gathered}\displaystyle\sf \dashrightarrow TSA = 2\pi \times r(28+6)\\\\\end{gathered}

⇢TSA=2π×r(28+6)

\begin{gathered}\displaystyle\sf \dashrightarrow TSA = 2\pi \times r(34)\\\\\end{gathered}

⇢TSA=2π×r(34)

\begin{gathered}\displaystyle\sf \dashrightarrow TSA = 2\pi \times 6\times 34\\\\\end{gathered}

⇢TSA=2π×6×34

\begin{gathered}\displaystyle\sf \dashrightarrow TSA = 2\pi\times 204\\\\\end{gathered}

⇢TSA=2π×204

\begin{gathered}\displaystyle\sf \dashrightarrow TSA = 2\times \frac{22}{7}\times 204\\\\\end{gathered}

⇢TSA=2×

7

22

×204

\begin{gathered}\displaystyle\sf \dashrightarrow TSA = 2\times 641.2\\\\\end{gathered}

⇢TSA=2×641.2

\begin{gathered}\displaystyle\sf \dashrightarrow\underline{\boxed{\sf TSA = 1282.4 \ cm^2}}\\\end{gathered}

⇢

TSA=1282.4 cm

2

\displaystyle\therefore\:\underline{\textsf{The TSA of the cylinder is \textbf{1282.4 cm}}\sf {}^2}∴

The TSA of the cylinder is 1282.4 cm

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