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 The following question has two statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.  The height of a right circular cone is ‘h’ and radius is ‘r’. A small cone is cut-off at the top by a plane parallel to the base. At what height above the base, the section has been made? I) Height of cone (h) = 40 cm II) Volume of smaller cone ∶ volume of larger cone = 1 ∶ 30

 The following question has two statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.  The height of a right circular cone is ‘h’ and radius is ‘r’. A small cone is cut-off at the top by a plane parallel to the base. At what height above the base, the section has been made? I) Height of cone (h) = 40 cm II) Volume of smaller cone ∶ volume of larger cone = 1 ∶ 30 Correct Answer Both I and II

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Considering statement, I,

Height of cone (h) = 40 cm

Considering statement II,

Volume of smaller cone∶ volume of larger cone = 1 ∶ 30

Let the radius and height of the smaller cone be r1 and h1 respectively.

⇒ (1/3πr12h1) ∶ (1/3πrh) = 1 ∶ 30

⇒ (r12h1) ∶ r2h = 1 ∶ 30

⇒ (r1/r)2 = (h/h1) × 1/30

Now,

When section is made, the two cones are similar triangles

⇒ r/r1 = h/h1

Considering both the statements,

⇒ h13/h3 = 1/30

⇒ h13 = (1/30) × (40)3 = 2133.34

⇒ h1 = 12.87 cm

∴ Both the statements are required to answer the question

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