Question

Find the volume of a cylinder whose circumference is 32cm and height is 25cm​

Answer 1

$\large{ \rm \underline{{Given - } }}$

$\sf \dashrightarrow Circumference \: of \: cylinder = 32 \: cm$

$\sf \dashrightarrow Height \: of \: cylinder = 25 \: cm$

$\large{ \rm \underline{{ To \: find - } }}$

$\sf \dashrightarrow Volume \: of \: cylinder = \: ?$

$\large{ \rm \underline{{Solution - } }}$

$\sf \dashrightarrow \underline{\boxed{ \sf Volume \: of \: cylinder = \pi r^2 h }}$

$\bf \underline{ Now},$

$\sf \dashrightarrow Circference \: of \: a \: cylinder = 32 \: cm$

$\sf \dashrightarrow 2 \pi r =32$

$\sf \dashrightarrow 2 \times \dfrac{22}{7} \times r =32$

$\sf \dashrightarrow r = \dfrac{ 32 \times 7}{22 \times 2}$

$\sf \dashrightarrow r = \dfrac{ 56}{11}$

$\sf \dashrightarrow r \approx 5.09 \: cm$

$\bf \underline{ Now},$

$\sf \dashrightarrow \sf Volume \: of \: cylinder = \pi r^2 h$

$\sf \dashrightarrow \sf \dfrac{22}{7} \times (5.09)^{2} \times 25$

$\sf \dashrightarrow \sf \dfrac{22}{7} \times 25.9081 \times 25$

$\sf \dashrightarrow \sf \dfrac{22 \times25.9081 \times 25 }{7}$

$\sf \dashrightarrow \sf \dfrac{14249.455 }{7}$

$\sf \dashrightarrow 2035.63$

$\bf \underline{ Therefore},$

$\boxed{ \sf The \: volume \: of \: the \: cylinder \: \approx \: 2035.63 \: cm ^3}$

━━━━━━━━━━━━━━━━━━━━━━━━

$\bf \: \underline{Some \: important \: terms}:$

$\sf \:1. \: Volume \: of \: Cylinder = \pi \: r^{2} \: h$

$\sf \: 2. \: Total \: Surface \: Area \: ( TSA ) \: of \: cylinder = 2 \pi \: r ( r + h )$

$\sf \:3. \: Curved \: Surface \: Area \: ( CSA ) \: of \: cylinder = 2 \pi \: r \: h$

$\sf \: 4. \: The \: value \: of \: \pi \: is \: \dfrac{22}{7} \: or \: 3.14 \: in \: decimal.$

$\bf \: \underline{Some \: other \: formulae}:$

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