An oil can is in the form of cylinderwhose radius is 7.7 cm and length

1.	An oil can is in the form of cylinderwhose radius is 7.7 cm and length is56 cm. Find the quantity of oil in litresthat can be stored in the can?
Answer» $\bf GivEn \begin{cases} & \sf{Radius\;of\;cylindrical\;oil\;can,\;r = \bf{7.7\;cm}} \\ & \sf{Height\;of\;cylindrical\;oil\;can,\;h = \bf{56\;cm}} \end{cases}\\ \\$ Need to FIND: The QUANTITY of oil in LITRES that can be STORED in the can. ⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━ $\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\$ Quantity of oil in that can be stored in can = Volume of oil can ⠀⠀ $\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\$ $\star\;{\boxed{\sf{\pink{Volume_{\;(cylinder)} = \pi r^2 h}}}}\\ \\$ Here, ⠀⠀ r = 7.7 cm h = 56 cm ⠀⠀ $\setlength{\unitlength}{1.3mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(16,2)(0,32){2}{\sf{\footnotesize 7.7 cm}}\put(14,17.5){\sf{\footnotesize 56 cm}}\end{picture}$ ⠀⠀ $\dag\;{\underline{\frak{Putting\;values\;in\;formula,}}}\\ \\$ $:\implies\sf Volume_{\;(oil\;can)} = \dfrac{22}{ \cancel{7}} \times 7.7 \times 7.7 \times \cancel{56}\\ \\ :\implies\sf Volume_{\;(oil\;can)} = 22 \times 7.7 \times 7.7 \times 8\\ \\ :\implies\sf Volume_{\;(oil\;can)} = 176 \times 7.7 \times 7.7\\ \\ :\implies{\underline{\boxed{\frak{\purple{Volume_{\;(oil\;can)} = 10435.04\;cm^3 }}}}}\;\bigstar\\ \\$ $\dag\;{\underline{\frak{Quantity\;of\;oil\;in\;<klux>LITRE</klux>,}}}\\ \\$ We know that, ⠀⠀ 1 Litre = 1000 cm³ ⠀⠀ $:\implies\sf Volume_{\;(oil\;can)} = 10.43504\;L\\ \\$ $\therefore$ Quantity of oil in litres that can be stored in the can is 10.43504 L. ⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━ $\boxed{\underline{\underline{\bigstar \: \bf\:Formulas\:related\:to\: cylinder\:\bigstar}}} \\ \\$ $\sf (i)\;Curved\;surface\;area\;of\;cylinder\; = \; \red{2 \pi rh}$ ⠀⠀⠀⠀⠀⠀⠀ $\sf (ii)\;Total\;surface\;area\;of\;cylinder\; = \; \purple{2 \pi r(h + r)}$ ⠀⠀⠀⠀⠀⠀⠀ $\sf (iii)\;Volume\;of\;cylinder\; = \; \pink{ \pi r^2 h}$

An oil can is in the form of cylinderwhose radius is 7.7 cm and length is56 cm. Find the quantity of oil in litresthat can be stored in the can?

Answer»

$\bf GivEn \begin{cases} & \sf{Radius\;of\;cylindrical\;oil\;can,\;r = \bf{7.7\;cm}} \\ & \sf{Height\;of\;cylindrical\;oil\;can,\;h = \bf{56\;cm}} \end{cases}\\ \\$

Need to FIND: The QUANTITY of oil in LITRES that can be STORED in the can.

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\$

Quantity of oil in that can be stored in can = Volume of oil can

⠀⠀

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\$

$\star\;{\boxed{\sf{\pink{Volume_{\;(cylinder)} = \pi r^2 h}}}}\\ \\$

Here,

⠀⠀

r = 7.7 cm
h = 56 cm

⠀⠀

$\setlength{\unitlength}{1.3mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(16,2)(0,32){2}{\sf{\footnotesize 7.7 cm}}\put(14,17.5){\sf{\footnotesize 56 cm}}\end{picture}$

⠀⠀

$\dag\;{\underline{\frak{Putting\;values\;in\;formula,}}}\\ \\$

$:\implies\sf Volume_{\;(oil\;can)} = \dfrac{22}{ \cancel{7}} \times 7.7 \times 7.7 \times \cancel{56}\\ \\ :\implies\sf Volume_{\;(oil\;can)} = 22 \times 7.7 \times 7.7 \times 8\\ \\ :\implies\sf Volume_{\;(oil\;can)} = 176 \times 7.7 \times 7.7\\ \\ :\implies{\underline{\boxed{\frak{\purple{Volume_{\;(oil\;can)} = 10435.04\;cm^3 }}}}}\;\bigstar\\ \\$