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    Surface Areas and Volumes
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    A hemispherical tank of radius 1.75 m is full of water it is connected with a pipe which empties it at the rate of 7 litres per second. How much time will it take to empty the tank completely.

    Solution not provided.

    Ans. 26.73 minutes

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    Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the birth - bath.   
    open parentheses bold pi bold space bold equals bold space bold 22 over bold 7 close parentheses bold space bold space

    Let r cm be the radius and h cm be the height of the cylinder then,
    r = 30 cm,
    h = 1.45 m = 145 cm.
    Lei r1 cm be the radius of the hemisphere, then
    r1 = 30 cm
    Now,
    The Total Surface Area of the bird bath
    = C.S.A of cylinder + C.S.A of Hemisphere
    = 2 straight pi rh + 2 straight pi r1 2
    = 2straight pirh + 2straight pir2    [∵ r = r1]
    = [2 ∵ r (h + r)] cm2

    equals space open square brackets open parentheses 2 straight x 22 over 7 straight x 30 close parentheses left parenthesis 145 space plus space 30 right parenthesis close square brackets space cm squared equals space open parentheses 1320 over 7 straight x 175 close parentheses space cm squared
    = 33000 cm2
    = 3.3 m2


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    Water flows through a circular pipe whose internal diameter is 2 cm at the rate of 0.7 m per second into a cylindrical tank, the radius of whose base is 40 cm By how much will the level of water rise in the tank in half an hour.

    Solution not provided.

    Ans. 78.75 m  

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    Water is flowing at the rate of 15 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm.

    Solution not provided.

    Ans. 2 m

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    Four right circular cylindrical vessels each having diameter 21 cm. and height 38 cm. are full of icecream. The icecream is to be filled in cones of height 12 cm and diameter 7cm having hemispherical shape at the top. Find the total number of such cones which can be filled with icecream.

    Solution not provided.

    Ans. 216

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