Question

94. A storage tank consists of a cylinder, with a hemisphere adjoined on either end (see fig). If the external diameter of the cylinder be 1.4m and its length are 5m. What will be the cost of painting it on the outside, at the rate of ₹10 per sq. meter​

Answer 1

$\large{\underline{\underline{ \bf{⎆Question:-}}}}$

• A storage tank consists of a cylinder, with a hemisphere adjoined on either end (see fig). If the external diameter of the cylinder be 1.4m and its length are 5m. What will be the cost of painting it on the outside, at the rate of ₹10 per sq. meter

$\large{\underline{\underline{ \bf{☂ Solution:-}}}}$

$\bold{ \large \underline{ \mathbb{\underline{✰GIVEN : }}}}$

$\tt{Diameter \: : 1.4m}$

$\tt{Therefore \: , Radius \:: 0.7m}$

$\tt{Height \: : 5m}$

$\bold{ \large \underline{ \mathbb{\underline{ ✰TO \: FIND : }}}}$

$\tt{The\:cost\:of\: painting\: on\:the \: outside\:@\:₹10/m².}$

• To find the cost , we have to calculate the total outer surface area of this solid .

$\tt{Total\:surface\:area\:of\:this \: solid\: \: :}$

• Surface area of cylinder + 2 ( Surface area of hemisphere)

$\tt{Required\: formula\::}$

$\huge\fbox\red{2 πrh + 2(2 π r²) }$

$\tt{ Where , \:h=Height\:and\:r=Radius.}$

$\small{\underline{\underline{ \bf{After\: putting\:the\:values:-}}}}$

$\tt{➥Area\:of\:solid\::}$

$\longmapsto\tt{2\:πrh +2( 2π {r}^{2} )u²}$

$\longmapsto\tt{2\pi \: r(h + r) {u}^{2} }$

$\longmapsto\tt{2 \times \frac{22}{7} \times 0.7(0.7 + 5) }$

$\longmapsto\tt{25.08 {m}^{2} }$

$\tt{∴ The \: cost \: of \: painting \: it \: on \: the \: outside \: at \: rate \: of \: @₹10/m² : }$

$\longmapsto\tt{25.08×₹10}$

$\longmapsto\tt{₹250.8}$