Question

An oil can is in the form of cylinder
whose radius is 7.7 cm and length is
56 cm. Find the quantity of oil in litres
that can be stored in the can?
​

Answer 1

Volume of Cylinder = πr²h

⇒ Volume of Cylinder = π × r² × h

⇒ Volume of Cylinder = 22/7 × r² × h

⇒ Volume of Cylinder = 22/7 × (7.7 cm)² × h

⇒ Volume of Cylinder = 22/7 × (7.7 cm)² × 56 cm

⇒ Volume of Cylinder = 22/7 × 59.29 cm² × 56 cm

⇒ Volume of Cylinder = 22/7 × 59.29 × 56 cm³

⇒ Volume of Cylinder = 10435.04 cm³

⇒ Volume of Cylinder = 10435.04 ml

⇒ Volume of Cylinder = 10.43504 L

Answer 2

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

Need to find: The quantity of oil in litres that can be stored in the can.

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

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

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

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

Here,

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• r = 7.7 cm
• h = 56 cm

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

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

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

$\dag\;{\underline{\frak{Quantity\;of\;oil\;in\;Litre,}}}$

We know that,

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• 1 Litre = 1000 cm³

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$:\implies\sf Volume_{\;(oil\;can)} = 10.43504\;L$

$\therefore$ Quantity of oil in litres that can be stored in the can is 10.43504 L.

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$\boxed{\underline{\underline{\bigstar \: \bf\:Formulas\:related\:to\: cylinder\:\bigstar}}}$

$\sf (i)\;Curved\;surface\;area\;of\;cylinder\; = \; \red{2 \pi rh}$

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$\sf (ii)\;Total\;surface\;area\;of\;cylinder\; = \; \purple{2 \pi r(h + r)}$

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$\sf (iii)\;Volume\;of\;cylinder\; = \; \pink{ \pi r^2 h}$