12. Two similiar cones have volumes 121 cu. units and 961 cu. units. I

1.	12. Two similiar cones have volumes 121 cu. units and 961 cu. units. Ifthe curved surface area of the smaller cone is 1571 sq. units, what isthe curved surface area of the larger one?
Answer» 1245224112344411123433221 Since the cones are similar so l₁/l₂ = r₁/r₂the the volumes are v₁12π unit³ , v₂ = 96π unit³so curved surface area = 15π unit² so v₂/v₁ = 96π/12π (πr₁²l₁)/(πr₂²l₂)= 8 cancelling 3 ⇒(r₂²l₂)/(r₁²l₁)= 8 ⇒ ⇒ r₂³/r₁³ = 8 usingl₁/l₂ = r₁/r₂ ⇒r₂/r₁ = 2 so curved surface area of the unknown cone be x so cs₂/cs₁ = x/15π ⇒πr₂l₂/πr₁l₁ =x/15π ⇒ r₂/r₁ x l₂/l₁ =x/15π ⇒ r₂²/r₁² = x/15π usingr₂³/r₁³ = 8 ⇒ 4 = x/15π ⇒ x = 60πANSWER 60π is correct answer

12. Two similiar cones have volumes 121 cu. units and 961 cu. units. Ifthe curved surface area of the smaller cone is 1571 sq. units, what isthe curved surface area of the larger one?

Answer»

1245224112344411123433221

Since the cones are similar so l₁/l₂ = r₁/r₂the the volumes are v₁12π unit³ , v₂ = 96π unit³so curved surface area = 15π unit²

so v₂/v₁ = 96π/12π (πr₁²l₁)/(πr₂²l₂)= 8 cancelling 3

⇒(r₂²l₂)/(r₁²l₁)= 8

⇒

⇒ r₂³/r₁³ = 8 usingl₁/l₂ = r₁/r₂

⇒r₂/r₁ = 2

so curved surface area of the unknown cone be x

so cs₂/cs₁ = x/15π

⇒πr₂l₂/πr₁l₁ =x/15π

⇒ r₂/r₁ x l₂/l₁ =x/15π

⇒ r₂²/r₁² = x/15π usingr₂³/r₁³ = 8

⇒ 4 = x/15π

⇒ x = 60πANSWER

60π is correct answer