Question

$\mathfrak\pink{Question ?}$

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

Given :

• Slant Height of tomb = 25 m
• Diameter of tomb = 14 m
• Rate of white - washing = Rs.210 per 100 m²

To Find :

• Cost of white - washing = ?

Solution :

$\red\clubs$ Formula Used :

• ${\underline{\boxed{\color{darkblue}{\sf{ Curved \; Surface \; Area{\small_{(Cone)}} = \pi rl }}}}}$

Where :

• ➻ ${\sf{ \pi = \dfrac{22}{7} }}$

• ➻ r = Radius
• ➻ h = Height

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$\red\clubs$ Calculating the CSA of Tomb :

${\longmapsto{\qquad{\sf{ CSA{\small_{(Tomb)}} = \pi rl }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ CSA{\small_{(Tomb)}} = \bigg\lgroup \dfrac{22}{7} \bigg\rgroup \times 25 \times \bigg\lgroup \dfrac{Diameter}{2} \bigg\rgroup }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ CSA{\small_{(Tomb)}} = \bigg\lgroup \dfrac{22}{7} \bigg\rgroup \times 25 \times \bigg\lgroup \dfrac{14}{2} \bigg\rgroup }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ CSA{\small_{(Tomb)}} = \bigg\lgroup \dfrac{22}{7} \bigg\rgroup \times 25 \times \bigg\lgroup \cancel\dfrac{14}{2} \bigg\rgroup }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ CSA{\small_{(Tomb)}} = \bigg\lgroup \dfrac{22}{7} \bigg\rgroup \times 25 \times 7 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ CSA{\small_{(Tomb)}} = \bigg\lgroup \dfrac{22}{\cancel7} \bigg\rgroup \times 25 \times \cancel7 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ CSA{\small_{(Tomb)}} = 22 \times 25 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\orange{\pmb{\frak{ Surface \; Area = 550 \; {cm}^{2} }}}}}}}}$

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$\red\clubs$ Calculating the Cost :

${\dashrightarrow{\qquad{\sf{ Cost{\small_{(White - washing)}} = CSA \times Rate }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Cost{\small_{(White - washing)}} = 550 \times \dfrac{210}{100} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Cost{\small_{(White - washing)}} = 550 \times \cancel\dfrac{210}{100} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Cost{\small_{(White - washing)}} = 550 \times 2.1 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\purple{\pmb{\frak{ Cost \; of \; White - wasing = ₹ \; 1155 }}}}}}}}$

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$\red\clubs$ Therefore :

❛❛ Cost of white - washing the Conical tomb is ₹ 1155 . ❜❜

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Answer 2

Answer:

Rs. 1155.

Step-by-step explanation:

We know, the curved surface area of a cone =πrl,

where r is the radius of the cone and l is the slant height.

Given, diameter of the tomb d=25m.

$Radius \: of \: the \: tomb = \frac{2}{d} =7m.$

Hence, Curved Surface Area of the conical tomb =

$</p><p> \frac{22}{7} ×7×25=550  sq. m.$

Cost of white washing the tomb at Rs. 210 per

$100m2= \frac{210}{100} ×550= Rs. 1155.$