MathematicsA right circular cone of radius 3 π‘π‘š, has a curved surface area ofΒ 47.1cm2Find the volume of the cone. (Use Ο€ = 3. 14)Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  (OR)In the given figure, βˆ†π‘ƒπ‘„π‘… is an equilateral triangle of side 8 π‘π‘š and 𝐷, 𝐸, 𝐹 are centres of circular arcs, each radius 4 π‘π‘š. Find the area of shaded region. (Use Ο€ = 3. 14 andΒ Β 3Β Β Β Β  = 1. 732)Β 

A right circular cone of radius 3 π‘π‘š, has a curved surface area of 47.1cm2

Find the volume of the cone. (Use Ο€ = 3. 14)

                                                (OR)

In the given figure, βˆ†π‘ƒπ‘„π‘… is an equilateral triangle of side 8 π‘π‘š and 𝐷, 𝐸, 𝐹 are centres of circular arcs, each radius 4 π‘π‘š. Find the area of shaded region. (Use Ο€ = 3. 14 and  3     = 1. 732)

 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    We need to find the volume of the cone of radius 3 π‘π‘š provided that its curved surface area of 47.1 cm2.
    It is known that the CSA of a cone is given as 𝐢𝑆𝐴 = Ο€π‘Ÿπ‘™, where π‘Ÿ and 𝑙 are the radius and slant height respectively.
    On substituting the values, we get the slant height as
    β‡’ 47. 1 = Ο€(3)𝑙
    β‡’ 47. 1 = 9. 42𝑙
    β‡’ 𝑙 = 5 π‘π‘š
    Now, the height of the cone can be given as
    β„Ž = 52-32
    β‡’ β„Ž = 16
    β‡’ β„Ž = 4 π‘π‘š
    Also, the volume of the cone is given by 𝑉 = 1/3Ο€π‘Ÿ2 h . On substituting the values, we get
    3 Ο€π‘Ÿ β„Ž
    β‡’ 𝑉 = 1/3 Ο€ x 3 x 4
    β‡’ 𝑉 = 37.68 cm3
    Hence, the volume of the cone is 37.68 cm3

     

                                                                               (OR)

     

    We need to find the area of shaded region provided that βˆ†π‘ƒπ‘„π‘… is an equilateral triangle of side 8 π‘π‘š and 𝐷, 𝐸, 𝐹 are centres of circular arcs, each radius 4 π‘π‘š.

    It can be observed that the arcs form the sector in the triangle and hence, the area of shaded region is

    π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ π‘ β„Žπ‘Žπ‘‘π‘’π‘‘ π‘Ÿπ‘’π‘”π‘–π‘œπ‘› = π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ†π‘ƒπ‘„π‘… βˆ’ 3(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ π‘ π‘’π‘π‘‘π‘œπ‘Ÿ)

    β‡’ π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ π‘ β„Žπ‘Žπ‘‘π‘’π‘‘ π‘Ÿπ‘’π‘”π‘–π‘œπ‘› = 34Γ—side2 - 3 Γ—ΞΈ360°×πr2

    β‡’ π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ π‘ β„Žπ‘Žπ‘‘π‘’π‘‘ π‘Ÿπ‘’π‘”π‘–π‘œπ‘› = 34Γ—82 - 3 Γ—60Β°360°×π42 163 - 8Ο€ 16 Γ— 1.732 - 8 x 3.14 27.712 - 25.12 2.592 cm2

    Hence, the area of the shaded region is  2.592 cm2.

    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.