SOLUTION: A hemispherical bowl of diameter 14cm mounted on a bucket in the form of a frustum of a cone. If the base diameter of the bucket is 7cm and the total height of the figure is 21cm,

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Question 1120123: A hemispherical bowl of diameter 14cm mounted on a bucket in the form of a frustum of a cone. If the base diameter of the bucket is 7cm and the total height of the figure is 21cm, calculate the total surface area of the figure. (Take pi = 22/7).
Answer by ikleyn(52787) About Me  (Show Source):
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1.  Base radius of the frustum cone is  r = 3.5 cm.

    The upper radius of the frustum cone is  R = 7 cm.

    The height of the frustum of the cone is  h = 21 - 7 = 14 cm.

    The slant height of the frustum of the cone is  s = sqrt%28%28R-r%29%5E2+%2B+h%5E2%29 = sqrt%283.5%5E2+%2B+14%5E2%29 = 14.43 cm  (approximately).



2.  The latent surface of the frustum of the cone is  

    A%5B1%5D = pi%2A%28R+%2B+r%29%2As = %2822%2F7%29%2A%287+%2B+3.5%29%2A14.43 = 476.19 square centimeters.

       (regarding this general formula see the link http://mathworld.wolfram.com/ConicalFrustum.html )



3.  The surface area of the semi-sphere is  A%5B2%5D = 2%2Api%2AR%5E2 = 2%2A%2822%2F7%29%2A7%5E2 = 308 square centimeters.


4.  The area of the base is  A%5B3%5D = pi%2Ar%5E2 = %2822%2F7%29%2A3.5%5E2 = 38.5 square centimeters.



5.  The answer to the problem question is the sum  


    A%5B1%5D + A%5B2%5D + A%5B3%5D = 476.19 + 308 + 38.5 = 822.69 square centimeters.

Solved.