Answer:

slant height ,

I = ✓r2 +h2, where h is the height of the cone

thus the cost of white washing the conical tomb is rs 1155

Answer:

Rs. 1155 will be the cost of white-washing the curved surface of a conical tomb at the rate of Rs. 210 per m².

Step-by-step explanation:

In the Question it is given that, the slant height of a conical tomb is 25m and its base diameter is 14m. We need to Find the cost of white-washing its curved surface at the rate of Rs. 210 per m².

As the tomb is in cone shape and we need to find the cost of white-washing its "Curved Surface". So, we will find the Curved Surface Area (C.S.A) of a cone by using Formula:

• C.S.A of a cone = πrl

Where,

• π = 22/7
• r = Radius
• l = Slant Height
• C.S.A = Curved Surface Area

Now, to Find Curved surface area (C.S.A) of a cone we should have:

• Value of π
• Radius
• Slant Height

And in the Question we are given with value of π, Slant Height and diameter but radius is not given. So, firstly we need to find the Radius of a cone by using Formula:

• [tex] \small \displaystyle\bf Radius = \frac{Diameter}{2} [/tex]

After finding Radius, we will find the C.S.A of a conical tomb and then after finding C.S.A of a conical tomb we will find the cost of white-washing its curved surface.

[tex] \bf Steps \: to \: Solve:- \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \small \sf Step 1: Find \: Radius \: of \: a \: Conical \: tomb. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \small \sf Step \: 2: Find \: C.S.A \: of \: a \: Conical \: tomb. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \small \sf Step \: 3: Find \: the \: cost \: of \: white-washing \: its \: curved \: surface.[/tex]

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[tex] \sf Solution:-[/tex]

Given-:

• Slant Height of a conical tomb (l) = 25m
• Base Diameter of a conical tomb (d) = 14m

To Find-:

• Cost of white-washing the curved surface of a conical tomb at the rate of Rs. 210 per m² = ?

Calculation-:

[tex] \small \sf Step \: 1: Finding \: Radius \: of \: a \: conical \: tomb: \\ \\ [/tex]

We know that,

• [tex] \small \displaystyle\bf Radius = \frac{Diameter}{2} \\ \\ [/tex]

Substituting values in the Formula:

[tex] \displaystyle \small\sf Radius = \frac{ \cancel{14} \: 7}{ \cancel{2}} \: \: \: \: \: \: \: \\ \\ \star \: \boxed{\bf \small Radius = 7m \: \: }[/tex]

• Radius of a conical tomb = 7m

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[tex] \small \sf Step \: 2: Finding \: C.S.A \: of \: a \: conical \: tomb: \\ \\ [/tex]

We know that,

• [tex] \small \sf C.S.A \: of \: a \: cone = πrl \\ \\ [/tex]

Substituting values in the Formula:

[tex] \displaystyle \small \sf C.S.A \: of \: a \: cone = \frac{22}{ \cancel{7}} \times \cancel{ 7 }\times 25 \: \: \: \: \: \: \\ \\ \small \sf C.S.A \: of \: a \: cone = 22 \times 25 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \small \bf C.S.A \: of \: a \: cone = 550m {}^{2} \: \: \: \: \: \: \: \: \: \: [/tex]

• C.S.A of a cone = 550 m².

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[tex] \small \sf Step \: 3: Finding \: the \: cost \: of \: white-washing \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \small \sf its \: curved \: surface \: at \: the \: rate \: of \: Rs. 210 \: per \: m²: \: \: \: \: \: \: \: [/tex]

[tex] \small \displaystyle \sf \rightarrow \: \frac{210}{10 \cancel{0}} \times 55 \cancel{0 }\\ \\ \sf \small \rightarrow \: \frac{21 \cancel{0} \times 55}{1 \cancel{0}} \: \: \\ \\ \small \sf \rightarrow \: 21 \times 55 \: \: \: \: \: \: \\ \\ \small \sf \rightarrow \:Rs. \: 1155 \: \: \: \: \: \\ \\ [/tex]

Hence, Rs. 1155 will be the cost of white-washing the curved surface of a conical tomb at the rate of Rs. 210 per m².