Math, asked by Anonymous, 4 months ago

Volume of a cylinder of height 50 cm is 1925 cube cm, find its diameter.
(a) 63 cm
(b) 71 cm
(c) 21 cm
(d) 87cm

Answers

Answered by danger7537
13

Answer:

your answer will be option D 87cm

Answered by DüllStâr
32

\bigstar \underline{\boxed{ \mathfrak {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{?cm(radius)}}\put(9,17.5){\sf{50cm(height)}}\end{picture}

\bigstar \underline{\boxed{ \mathfrak {Question: }}}

Volume of a cylinder of height 50 cm is 1925 cube cm, find its diameter.

[Note:your options were incorrect so I just ignored it]

\bigstar \underline{\boxed{ \mathfrak {Given: }}}

  • height of cylinder = 50cm
  • Volume of Cylinder = 1925 cm³

\bigstar \underline{\boxed{ \mathfrak {To\:find:}}}

  • diameter of Cylinder

\bigstar \underline{\boxed{ \mathfrak {Answer: }}}

 \underline{ \underline{ \bf{}we \: know: }}

\bigstar \boxed{\sf{}Volume \: of \: a \: cylinder = \pi r {}^{2} h}

By using this formula we can find value of radius.

 :  \implies\sf{}Volume \: of \: a \: cylinder = \pi r {}^{2} h

put values of volume of Cylinder and height .

: \implies\sf{}1925 =  \dfrac{22}{7} \times r {}^{2} \times 50

: \implies\sf{}1925  \times  \dfrac{7}{22}  \times  \dfrac{1}{50} =  r {}^{2}

: \implies\sf{} \cancel{1925} {}^{ \:  \: 77}  \times \dfrac{7}{22} \times \dfrac{1}{ \cancel{50} {}^{ \:  \: 2} } = r {}^{2}

 \sf : \implies   \dfrac{77 \times 7}{22 \times 2}  =  {r}^{2}

 \sf :\implies\dfrac{539}{44} =  {r}^{2}

 \sf :\implies12.25=  {r}^{2}

\sf :\implies \sqrt{12.25}= {r}

\sf :\implies \:  \underline{\boxed{  \sf \: r = 3.5cm}}

Now as we know radius is half of diameter :

\bigstar \boxed{\sf{} \therefore \: diameter =2 \times radius }

By using this equation we can find value of diameter.

\sf{}: \implies\: diameter =2 \times radius

Put value of radius in this equation

\sf{}: \implies\: diameter =2 \times 3.5

\sf :\implies\underline{\boxed{  \sf \: diameter = 7cm}}

\bigstar \underline{\boxed{ \mathfrak {Additional\:information:}}}

\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}}

And all we are done! ✔

:D

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