Question

The area of the sector shaped canvas cloth is 264 m² with this canvas cloth, if a right circular conical tent is erected with the radius of the base as 7 cm then find the height of the tent.​

Answer 1

$\tt{\huge{\pink{Hello!!! }}}$

Question :

The area of the sector shaped canvas cloth is 264 m² with this canvas cloth, if a right circular conical tent is erected with the radius of the base as 7 cm then find the height of the tent.

Solution :

According to the question ,

Area of Sector = LSA of Cone.

$</p><p>\tt{\purple{---------}}$

Given :

• R = 7 cm = 0.07 m.

• L.S.A = 264 m^2

• H = ?

$</p><p>\tt{\purple{---------}}$

We know that :

$\tt{ \purple{ \implies{L.S.A \: of \: Cone \: = \: \pi \: r \: l \: }}}$

$\tt{ \orange{\pi \: r \: l \: = 264 }} \\ \\ = > </p><p></p><p>=> 0.07 × 22 / 7 × l = 264</p><p></p><p>=> 0.01 × 22 × l = 264</p><p></p><p>=> l = 264 / 0.22 m</p><p></p><p>[tex]</p><p>\tt{\purple{---------}}$

Hence :

$\tt{ \green{ \implies{l \: = 1200 \: m.}}}$

We know that :

$\tt{ \red{ {l}^{2} = {r}^{2} + {h}^{2} }} \\ \\ = > \tt{ \blue{ \implies{h \: = \sqrt{ {L}^{2} \: - \: {r}^{2} } = \sqrt { {1200}^2 - {0.07}^2 } = \sqrt{\1200.07}{1199.33} approx \: 1199.99 \: m. }}}$

$</p><p>\tt{\purple{---------}}$

$\tt{\orange{Additional\: Information\: : }}$

$</p><p>\tt{\blue{\disc{Volume \: Of \: A \: Cone = \dfrac{1}{3} \pi {r}^2 h }}}$

$</p><p>\tt{\blue{\disc{CSA \: Of \: A \: Cone = \pi\: r\: l }}}$

$</p><p>\tt{\purple{---------}}$

Answer 2

Answer:

1199.99 m

Step-by-step explanation:

Given :

Area of the sector shaped canvas cloth = 264 m²

It is also equal to curved surface area of cone :

= > π r l = 264 m²

We have radius r = 7 cm = 0.07 m

= >  0.07 × 22 / 7 × l = 264

= > 0.01 × 22 × l = 264

= > l = 264 / 0.22 m

= > l = 1200 m

We have relation between h , r and l :

= > l² = h² + r²

= > h² = l² - r²

= > h² = 1200² - 0.07² m

= > h² = ( 1200 + 0.07 ) ( 1200 - 0.07 ) m

= > h² = ( 1200.07 ) ( 1199.93 ) m

= > h = √ ( 1200.07 ) ( 1199.93 ) m

= > h = 1199.99 m

Hence we get required answer.

When the radius in unit of meter i.e. 7 m : then let's find height h :

π r l = 264 m²

We have r = 7 m

= > 22 / 7 × 7 × l = 264

= > l = 264 / 22 m

= > l = 12 m

We know :

l² = h² + r²

= > h² = l² - r²

= > h² = 12² - 7²

= > h² = ( 12 + 7 ) ( 12 - 7 )

= > h = √ ( 19 × 5 ) m

= > h = √ 95 m.