Question

A conical tent is 10m high and the radius of its base is 24m find (i)slant height of the tent (ii) cost of canvas required to make the tent is the cost of 1m² canvas is rupee 17​

Answer 1

Solution :-

Height of the conical tent ( h ) = 10 m

Radius of its base ( r ) = 24 m

Let the slant height be l

l = √( r² + h² )

⇒ l = √( 24² + 10² )

⇒ l = √( 576 + 100 )

⇒ l = √676

⇒ l = 26 m

Canvas required to make the tent = Curved Surface Area ( CSA ) of the conincal tent

CSA of the conical tent = πrl

= ( 22/7 ) * 24 * 26

= ( 22/7 ) * 624

= 13728/7

= 1961.14 ( approximately )

Cost of 1 m² canvas = Rs. 17

Cost of canvas required to make the tent = 1961.14 * 17 = Rs. 33339.38

Hence, slant height of the tent is 26 m and cost of the canvas required to make the tent is Rs. 33339.38.

Answer 2

Answer:-

→ Slant height of tent is 26 m

→Cost required to make it Rs 33339.38

To Find :-

→ (1) Slant height of tent

→ (2) Cost of canvas

Formula used :-

$\small \sf{slant \: height \: = \sqrt{ {(radius)}^{2} + {(height)}^{2} } }$

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Step - by - step explanation :-

• Height of tent (h) = 10 m

• Radius of its base (r) = 24 m

• Slant height ( l ) = ?

Using the given formula to finding the slant height ,

$\rightarrow \sf{ l \: = \sqrt{ {(10)}^{2} + {(24)}^{2} } }\\ \\ \rightarrow \sf{ l \: = \sqrt{100 + 576} } \\ \\ \rightarrow \sf{l \: = \sqrt{676} } \\ \\ \rightarrow \boxed{\sf{ l \: = 26}}$

Slant height is 26 m .

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Curved surface area of conical tent

$\implies \sf{ \pi \: r \: l} \\ \\ \implies \: \frac{22}{7} \times 24 \times 26 \\ \\ \implies \: \frac{13728}{7} \\ \\ \implies \sf{ 1961.14 \: \: {m}^{2} }$

Curved surface area of tent is 1961.14 m^{2} .

$\sf{cost \: of \: 1 \: {m}^{2} \: canvas \: = 17 \: } \\ \\ \sf{ total \: cost \: required \: to \: make \: tent} \\ \\ \implies \: 1961.14 \times 17 \\ \\ \implies \:Rs \: 33339.38$

Total cost required to make tent is

Rs. 33339.38

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