Question

the diametre of the base of right circular cone is21 metres and height 14 metre.what will be the exenditure to colour the curved surface at the rate of. rs 1.50 per square metre?​

Answer 1

$\sf\large{\green{\underbrace{ Expenditure \implies Rs.\:173.2}}}$

$\sf\large{ \: \: }$

$\sf\large{\underline{\underline{Given:}}}$

$\sf\large{Diameter\:of\:the\:base\:of\:Right\:Circular\:Cone = 21\:m}$

$\sf\large{Height= 14\:m}$

$\sf\large{Rate\:to\:color\:the\:C.S.A = Rs.\:1.50\: per\:sq.m}$

$\sf\large{ \: \: }$

$\sf\large{\underline{\underline{Solution:}}}$

$\sf\large{ \: \: \: Let,\:base\:radius\:of\:the\:cone = r\:m}$

$\sf\large{ \: \: }$

$\sf\large{\underline{\underline{According\:To\:Problem:}}}$

$\sf\large{\red{\implies pie {r}^{2} = 21}}$

$\sf\large{\purple{\implies {r}^{2} = 21 × \dfrac{7}{22}}}$

$\sf\large{\orange{\implies r = 2.58}}$

$\sf\large{ \: \: }$

$\sf\large{\underline{\underline{Therefore:}}}$

$\sf\large{ \: \: \: Radius\: of\:the\:base = 2.58m}$

$\sf\large{ \: \: \: Height \: if \: the\:cone = 14m}$

$\sf\large{ \: \: }$

$\sf\large{\therefore{Slant\:height\:of\:the\:cone,}}$

$\sf\large{\red{ = \sqrt{{2.58}^{2} + {14}^{2}}}}$

$\sf\large{\purple{= \sqrt{6.66 + 196}}}$

$\sf\large{\orange{ = 14.24\:cm}}$

$\sf\large{ \: \: }$

$\sf\large{\therefore{"curved\:surface\:area\:of\:cone,}}$

$\sf\large{\red{ = pie\:rl}}$

$\sf\large{\purple{ = \dfrac{22}{7} × 2.58 × 14.24}}$

$\sf\large{\orange{ = 115.47\:sq.m}}$

$\sf\large{ \: \: }$

$\sf\large{\underline{\underline{Therefore}}}$

$\sf\large{ \: \: \: Expenditure\:to\:color\:the\:curved\:surface\:area,}$

$\sf\large{\red{ = 115.47 × 1.50}}$

$\sf\large{\green{ = Rs.\:173.2}}$