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Charlie is making a toy silo for his children. The silos height is three times it's radius. He is also adding a dome shaped top that is a half sphere. If the total surface area of the silo, when assembled is 100 square inches , what is the height of the silo(i.e., what is the distance from the base of the silo to the tip of the dome shaped top)?

  • Math -

    I see the surface area as the
    circular area of the base + rectangle + 1/2 surface area of the sphere
    let the radius be r and the height be h
    so we want to measure h+r

    given:
    " the silo's height i three times its' radius" ---> h+r = 3r
    h = 2r

    πr^2 + 2πrh + (1/2) 4πr^2 = 100
    πr^2 + 2πr(2r) + 2πr^2 = 100
    7πr^2 = 100
    r^2 = 100/(7π)
    r = 2.1324 inches
    h = 4.2648 inches

    so the height of the toy silo = r+h = 6.397
    or appr 6.4 inches

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