Question

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

Answer 1

Answer:

your answer will be option D 87cm

Answer 2

$\bigstar \underline{\boxed{ \mathfrak {Diagram:}}}$

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{?cm(radius)}}\put(9,17.5){\sf{50cm(height)}}\end{picture}$

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

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