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Math - function problems

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1) A box with a square base has a total surface area of 12m^2. Express the volume of the box as a function of the base edge.

2) A 10 foot tall lamppost causes a child 4 feet tall to cast a shadow of x feet on the ground. If the distance along the ground from the child to the lamppost is d meters, express x as a function.

  • Math - function problems -

    let the side of the square base be x m
    let the height be y m

    I will assume the box has a lid so the surface area is made up of 2x^ + 4xy
    then 2x^2 + 4xy = 12
    4xy = 12-2x^2
    y = (6-x^2)/(2x)

    volume = x^2y
    = x^2(6-x^2)/(2x)
    = x(6-x^2)/2

    for the second, you have similar triangles, so set up a ratio
    4/x = 10/(x+d)
    10x = 4x + 4d

    take it from there

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