Math

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1)Forty solid hemisphere each of diameter 2cm , are melted to form a solid cone with a base diameter 6cm .Find the height of the cone?

2)A pyramid has a square base of side 12cm and a height of 15cm .Calculate its volume and total surface area?

  • Math -

    V = 40 (4/3) pi r^3
    r = 1
    V = (160/3) pi

    V = (1/3)pi r^2 h

    (160/3) pi = (1/3) pi 3^2 h
    160 = 9 h
    h = 160/9

    2)
    (1/3) 144 (15) = V

    distance up slope of side :
    15^2 + 6^2 = L^2
    L = sqrt (225+36) = sqrt(261)
    area of one side = (1/2)(12)sqrt 261
    area of 4 sides = 24 sqrt 261
    It is not clear if we should add the bottom area
    If so then 144+24 sqrt 261

  • Math -

    1) 8.88

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