If the ratio between the curved surface area of two cones is 5 ∶ 39

1.	If the ratio between the curved surface area of two cones is 5 ∶ 39 and the ratio between their radius is 1 ∶ 3. Find the ratio between their slant height.1. 7 ∶ 122. 5 ∶ 133. 13 ∶ 54. 12 ∶ 13
Answer» Correct Answer - Option 2 : 5 ∶ 13 Given: Ratio between CSA = 5 ∶ 39 Ratio between diameters = 1 ∶ 3 Formula used: CSA of cone = πrl, where l is slant height and r is the radius of the base. Calculation: Let the l₁ and l₂ be the slant height of two cones. Curved surface area of cone 1, CSA₁ = πR₁l₁ Curved surface area of cone 2, CSA₂ = πR₂l₂ According to the question, CSA₁/CSA₂ = 5/39 ⇒ (πR₁l₁)/( πR₂l₂) = 5/39 ⇒ R₁/R₂ × l₁/l₂ = 5/39 ⇒ 1/3 × l₁/l₂ = 5/39 ⇒ l₁/l₂ = 5/13 ∴ The ratio between their slant height is 5 ∶ 13.

If the ratio between the curved surface area of two cones is 5 ∶ 39 and the ratio between their radius is 1 ∶ 3. Find the ratio between their slant height.1. 7 ∶ 122. 5 ∶ 133. 13 ∶ 54. 12 ∶ 13

Answer» Correct Answer - Option 2 : 5 ∶ 13

Given:

Ratio between CSA = 5 ∶ 39

Ratio between diameters = 1 ∶ 3

Formula used:

CSA of cone = πrl, where l is slant height and r is the radius of the base.

Calculation:

Let the l₁ and l₂ be the slant height of two cones.

Curved surface area of cone 1, CSA₁ = πR₁l₁

Curved surface area of cone 2, CSA₂ = πR₂l₂

According to the question,

CSA₁/CSA₂ = 5/39

⇒ (πR₁l₁)/( πR₂l₂) = 5/39

⇒ R₁/R₂ × l₁/l₂ = 5/39

⇒ 1/3 × l₁/l₂ = 5/39

⇒ l₁/l₂ = 5/13

∴ The ratio between their slant height is 5 ∶ 13.

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