MathematicsIn the figure given below, a decorative block is shown which is made of two solids, a cube and a hemisphere. The base of the block is a cube with an edge of 6cm and the hemisphere fixed on the top has a diameter of 4.2cm. Find the total surface area of the block.

In the figure given below, a decorative block is shown which is made of two solids, a cube and a hemisphere. The base of the block is a cube with an edge of 6cm and the hemisphere fixed on the top has a diameter of 4.2cm. Find the total surface area of the block.


  1. A
    329.86c m 2  
  2. B
    229.86c m 2  
  3. C
    429.86c m 2  
  4. D
    529.86c m 2   

    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:

    Given,
    Decorative block is made up of a cube and a hemisphere.
    The diameter of the hemisphere = 4.2cm
    The edge of the cube = 6cm
    The formula for the total surface area of a cube is 6 a 2   where a is the edge of the cube. The formula for the curved surface area of a hemisphere of radius, r is given by 2π r 2   . The radius is half of the diameter.
    We have to find the total surface area of the block.
    As, the diameter of the hemisphere = 4.2cm, so the radius of the hemisphere is      r= 4.2 2 r=2.1cm  
    The curved surface area of the hemisphere is given by CSA=2π r 2  .
    We get,
    CSA=2π (2.1) 2 CSA=2× 22 7 ×2.1×2.1 CSA=27.72c m 2  
    Now, the edge of a cube is 6cm.
    The total surface are of a cube of edge a is given by TS A c =6 a 2  
    We get,
    TS A c =6 6 2 TS A c =6×6×6 TS A c =216c m 2  
    The total surface area of the block = total surface area of cube – base area of hemisphere + curved surface area of hemisphere
    Base area of hemisphere is A b =π r 2  
    We get,
    A b = 22 7 × (2.1) 2 A b = 22 7 ×2.1×2.1 A b =13.86c m 2  
    The total surface area of the block = =TS A c A b +CSA  
    We get,
    TSA=21613.86+27.72 TSA=229.86c m 2  
    Thus, the total surface area of the block is 229.86c m 2   .
    Hence, the correct option is 2.
     
    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.