Question

A Cylindrical Tank has a capacity of 6160 meter cube. Find Its Depth if its radius is 14m.Also Find the cost of painting it's curved surface at Rs. 3 per meter Square​

Answer 1

$\large\bf\underline\red{Question ➡} \\ \\ \sf \: A \: Cylindrical \: Tank \: has \: a \: capacity \: \\ \sf \: of \: 6160 \: {m}^{3} . \: Find \: Its \: Depth \: if \: its \\ \sf \: radius \: is \: 14m. \: Also \: Find \: th e \: cost \: \\ \sf \: of \: painting \: it's \: curved \: surface \: \\ \sf \: at \: Rs. \: 3 per \: meter \: Square \: . \\ \\ \\ \large\bf\underline\red{we \: have \: ➡} \\ \\ ➙ \: \: \sf \: volume \: of \: cylinder \: = 6160 \: {m}^{3} \\ \\ ➙ \: \: \sf \: radius \: of \: cylinder \: = 14 \: m \: \\ \\ \\ \large\bf\underline\red{to \: find \: ➡} \\ \\ ➥ \: \sf \: height \: of \: the \: cylindrical \: tank \: \\ \\ ➥ \: \sf \: cost \: \sf \: of \: painting \: it's \: curved \: \\ \sf \: \: \: \: surface \: \sf \: at \: Rs. \: 3 \: per \: {m}^{3} \: . \\ \\ \\ \\ \large\bf\underline\red{for \: finding \: height \: ➡} \\ \\ \bf \: volume \: of \: cylinder \: = \sf \: \pi {r}^{2} h \\ \\ \\ \bf \underline{put \: the \: above \: value \: we \: get \: } \\ \bf \underline { the \: value \: of \: height \: of \:tank \: - } \\ \\➳ \sf \: \pi {r}^{2} h \: = 6160 \\ \\ ➳ \sf \: \frac{22}{7} \times 14 \times 14 \times h = 6160 \\ \\ ➳ \sf \: \frac{22}{¹ \: \cancel7} \times ² \: \cancel{14} \times 14 \times h \: = 6160 \\ \\➳ \sf \: 44 \times 14 \times h = 6160 \\ \\ ➳\sf \: h = \frac{6160}{44 \times 14} \\ \\ ➳\sf \: h \: = \frac{ ⁴⁴⁰ \: \cancel{6160}}{44 \times ¹ \: \cancel{14} } \\ \\ ➳ \sf \:h = \frac{¹ ⁰ \: \cancel{440}}{¹ \: \cancel{44}} \\ \\ ➳ \sf \: h \: = 10 \: m \: \\ \\ \sf \: there fore \: the \: height \: of \: the \: \\ \sf \: tank \: is \: \large{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{10 \: m}}}} \\ \\ \\ \bf \underline{ now \: we \: have \: to \: find \: cost \: of} \: \\ \bf \underline{ \: painting \: it's \: curved \: surface \: } \\ \bf \underline{ at \: Rs. \: 3 per \: meter \: Square \: . } \\ \\ \\ \large\bf\underline\red{now \: we \: have \: ➡} \\ \\ ➙ \: \bf \: height \: of \: tank \: = \sf10 \: m \: \\ ➙ \bf \: radius \: of \: tank \: = \sf \: 14 \: m \\ \\ \\ \bf \underline{ for \: finding \: the \: cost \: of} \: \\ \bf \underline{ \: painting \: it's \: curved \: surface \: } \\ \bf \underline{ at \: Rs. \: 3 per \: meter \: Square \: } \\ \bf\underline{we \: have \: to \: find \: out \: the \:CSA } \\ \bf\underline{of \: the \: tank \: and \: multiply \: by \: the \: }\\ \bf\underline{ given \: cost} \\ \\ \\ \fbox\red{ CSA \: of \: cylinder = \: 2Πrh } \\ \\ \\ \sf \underline{put \: the \: above \: value \: we \: get : } \\ \\ \\ ➳ \sf \: 2 \pi rh =2× \frac{22}{7} \times 14 \times 10 \\ \\➳ \sf \: 2× \frac{22}{ ¹ \: \cancel7} \times ² \: \cancel{14} \: \times 10 \\ \\ ➳ \sf \: = 880 \: {m}^{2} \\ \\ \\ ➳ \sf \: \therefore \: the \:CSA \: of \: cylindrical \: tank = \small{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{880 \: m²}}}} \\ \\ \\ \sf \: so \: cost \: of \: painting \: at \: the \: rate \ \: of \\ \sf \: 3 \: {m}^{2} \: ➠ \: ➠ \\ \\ \sf \: 880 \times 3 = \bf \: 26400 \\ \\ \\ \sf \: cost \: of \: painting \: the \: tank \: is \: \small{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{2640 \: Rs}}}}$.