Question

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The curved surface area of a cone is 12320 sq. cm, if the radius of its base is 56 cm, find its height.

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Answer 1

Step-by-step explanation:

radius of the base of the cone = 56cm

We know that curve d surface area of a cone =πrl.

Given that curved surface area of a cone = 12320.

πrl= 12320

22/7 * 56* l=12320

22 * 8 * l=12320

176*l= 12320

l=12320/ 176 =70

We know that height of the cone,

h = √l^2-r^2

= √70²-56²

= √4900 - 3136

= √1764

= 42.

Therefore the height of the cone =

42m.

Answer 2

Given :

• The curved surface area of a cone is 12320 sq. cm, if the radius of its base is 56 cm.

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To Find :

• Height of the cone ?

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SolutioN :

• Let us assume that, the slant height of a cone is x cm.

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${\bf{\dag}}$ Formula Used :

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$\qquad\star~{\underline{\boxed{\pmb{\sf{CSA~of~cone~=~πrl}}}}}$

$\qquad\star~{\underline{\boxed{\pmb{\sf{l^2~=~h^2~+~r^2}}}}}$

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${\bf{\dag}}$ According to the Question :

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$\qquad{\sf\dashrightarrow{12320~=~πrl}}$

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$\qquad{\sf\dashrightarrow{12320~=~\dfrac{22}{\cancel{7}}~×~\cancel{56}~×~x}}$

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$\qquad{\sf\dashrightarrow{12320~=~22~×~8~×~x}}$

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$\qquad{\sf\dashrightarrow{12320~=~176~×~x}}$

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$\qquad{\sf\dashrightarrow{12320~=~176x}}$

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$\qquad{\sf\dashrightarrow{x~=~\cancel\dfrac{12320}{176}}}$

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$\qquad\dashrightarrow{\pmb{\underline{\boxed{\purple{\frak{x~=~70 }}}}}}$★

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Therefore,

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$\qquad$ ∴ The length of the cone is 70 cm.

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Now,

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$\qquad{\sf:\implies{(70)^2~=~h^2~+~(56)^2}}$

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$\qquad{\sf:\implies{4900~=~h^2~+~(56)^2}}$

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$\qquad{\sf:\implies{4900~=~h^2~+~3136}}$

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$\qquad{\sf:\implies{h^2~=~4900~-~3136}}$

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$\qquad{\sf:\implies{h^2~=~1764}}$

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$\qquad{\sf:\implies{h~=~\sqrt{1764}}}$

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$\qquad:\implies{\pmb{\underline{\boxed{\pink{\frak{h~=~42 }}}}}}$★

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Hence,

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$\qquad$ ∴ The height of the cone is 42 cm.

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