Question

$\huge \bf Question$

● The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs.210 per 100 sq.m.

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Answer 1

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Answer 2

${\underline{\underline{\rm{Understanding \: the \: Question:}}}}$

• According to the Question, it is given that a conical means cone shaped tomb has Slant height of 25 m and Diameter of 14 m. Also, rate of white washing of the tomb is Rs 210 for 100 m². In this we need to find Cost.

• We can find Surface Area by applying the formula and we have to find rate of white- washing the tomb of 1 m². It will be multiplied by the Area and Rate which will give cost of White - Washing.

${\underline{\underline{\rm{Given :}}}}$

• Slant Height = 25 m
• Base Diameter = 14 m
• Rate of White - Washing = 210 per 100 sq.m.

${\underline{\underline{\rm{To \: find :}}}}$

• Cost of white-washing.

$\rule{ 150}{2}$

${\underline{\underline{\rm{Solution :}}}}$

● At first we have to find Radius :

${\sf{\ratio{\longmapsto{ Radius = \dfrac{Diameter}{ 2 }}}}} \\ \\ {\sf{\ratio{\longmapsto{ Radius = \dfrac{14}{ 2 }}}}} \\ \\ { \underline{ \boxed{\sf{\ratio{\longmapsto{ Radius = 7 \: m \:}}}} }}$

$\rule{ 150}{2}$

● Second we have to find Surface Area of Conical tomb :-

${\sf{\ratio{\longmapsto{ Curved \: Surface \: Area =\pi rl \: }}}}$

Where as,

• r = Radius
• l = Slant Height

${\sf{\ratio{\longmapsto{ Curved \: Surface \: Area = \frac{22}{7} \times 7 \times 25 }}}} \\ \\ {\sf{\ratio{\longmapsto{ Curved \: Surface \: Area = 22\times 25 }}}} \\ \\ { \underline{ \boxed{\sf{\ratio{\longmapsto{ Curved \: Surface \: Area = 550 \: {m}^{2} }}}}}}$

$\rule{ 150}{2}$

● Third we have to find Rate of White washing for 1 m

${\rm{\longmapsto{ Rs.210 = 100 \: sq.m. }}} \\ {\rm{\longmapsto{ Rs \: ? = \: 1 \: sq.m. }}}$

By Cross multiplying them

${\rm{ \longmapsto{ Rs \: for \: 1 m^2 = \cfrac{ 210 \times 1}{100} }}} \\ \\ {\rm{ \longmapsto{ Rs \: for \: 1 m^2 = \cfrac{ 21 }{10} }}} \\ \\ { \underline{ \boxed{\rm{ \longmapsto{ Rs \: for \: 1 m^2 = 2.1 \:Rs}}}}}$

● So, Cost of White Washing is :-

${\large{ \bf{\ratio{\longmapsto{ Cost = Rate \times Area }}}}} \\ \\ {\large{ \bf{\ratio{\longmapsto{ Cost = 2.1 \times 550}}}}} \\ \\ { \underline{ \boxed{ \red{\large{ \bf{\ratio{\longmapsto{ Cost = 1155 \: Rs }}}}} }}}$

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MORE TO KNOW :-

$\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA=\pi r^2+\pi rl\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\\ \\{\textcircled{\footnotesize\textsf{5}}} \: \:Slant \: Height=\sqrt{r^2 + h^2}\end{minipage}}$