Question

The diameter of a cylinder is 60 cm and the height of the cylinder is
7 cm. Find the volume of the cylinder,​

Answer 1

Solution :

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{30 \: cm}}\put(9,17.5){\sf{7 \: cm}}\end{picture}$

The diameter of the cylinder is 60 cm .

Therefore the radii is 30 cm .

The height of the cylinder is 7 cm .

Volume of a cylinder -

> π r² h

> 22/7 × 30 × 30 × 7

> 22 × 900

> 19800 cm³ .

This is the required answer !

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Additional Information -

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

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

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Answer 2

To find :-

• Volume of the cylinder

Given :-

• Diameter of a cylinder = 60 cm
• Height of the cylinder = 7 cm

Solution :-

• Here we have diameter and height of the cylinder so firstly we will find the radii of the cylinder and then by using volume of the cylinder .

$\rule{300}{5}$

Finding radii of the cylinder :-

$\sf{Radii\:=\:\dfrac{Diameter}{2}}$

$\sf{Radii\:=\:\dfrac{60}{2}}$

$\sf{Radii\:=\:30cm}$

∴ radii of the cylinder is 30 centimeters .

$\rule{300}{5}$

Finding volume of the cylinder :-

$\mathsf{Volume\:of\:the\:cylinder\:=\:\pi \:r^2\:h}$

$\mathsf{Volume\:of\:the\:cylinder\:=\:\dfrac{22}{7}\:\times\:(30)^2\:\times\:7}$

$\mathsf{Volume\:of\:the\:cylinder\:=\:22\:\times\:(30)^2}$

Square of 30 is 900

$\mathsf{Volume\:of\:the\:cylinder\:=\:22\:\times\:900}$

$\mathsf{Volume\:of\:the\:cylinder\:=\:19,800\:cm^3}$

∴ volume of the cylinder is 19,800cm³