The volume and curved surface area of a cone are same. If the product of radius and height of the cone is

36 cm, then

2 thoughts on “The volume and curved surface area of a cone are same. If the product of radius and height of the cone is <br /><br /> 36 cm, then”

1. Given :-

   Volume and CSA of cone is same

   Product of radius and height = 36

   To find :-

   Slant height

   Solution :-

   Let

   [tex]\mid \pmb {Radius = r}\mid[/tex]

   [tex]\mid \pmb{Height = h}\mid[/tex]

   [tex]\mid \pmb{Slant \; height = l}\mid[/tex]

   [tex]\sf Volume \; of \; cone = CSA\; of \; cone[/tex]

   [tex]\sf \dfrac{1}{3} \pi r^2h = \pi rl[/tex]

   [tex]\sf \pi r^2 h = \pi rl \times 3[/tex]

   [tex]\sf r h = 3l[/tex]

   [tex]\sf 36 = 3l[/tex]

   [tex]\sf l = \dfrac{36}{3}[/tex]

   l = 12 cm

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2. Answer:

   • The slant height of the cone is 12 cm.

   Step-by-step explanation:

   Given that:

   1. The volume and curved surface area of a cone are same.
   2. The product of radius and height of the cone is 36 cm.

   To Find:

   • The slant height of the cone.

   Finding the slant height of the cone:

   Volume of a cone = Curved surface area of a cone

   ⟶ (πr²h)/3 = πrl

   ⟶ πr²h = 3πrl

   Cancelling π and r both sides.

   ⟶ rh = 3l

   ⟶ 36 = 3l [Given]

   ⟶ l = 36/3

   ⟶ l = 12

   ∴ The slant height of the cone = 12 cm

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