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  1. #1
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    Math help

    I want to know how to solve such questions:

    1) The radius r of a cylinder is increasing at the rate of 1cm/s and the volume V is decreasing at the rate of 1 cm^3 /s. where r=1 and h=2, find the rates of change of:

    (i) the height h
    (ii) the surface area S

    Note that V=\pi r^2 h and S=2\pi r^2 + 2\pi rh





    2) The region R in the first quadrant is bounded by the y-axis, the line y=x and the curve y=2- x^2. Calculate the volume formed when R is rotated about the y-axis through 1 revolution.

    (what should I do after finding the area? )
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  2. #2
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    Hello,
    Quote Originally Posted by Musab View Post
    I want to know how to solve such questions:

    1) The radius r of a cylinder is increasing at the rate of 1cm/s and the volume V is decreasing at the rate of 1 cm^3 /s. where r=1 and h=2, find the rates of change of:

    (i) the height h
    (ii) the surface area S

    Note that V=\pi r^2 h and S=2\pi r^2 + 2\pi rh
    Let V(t)=\pi r^2(t) h(t)

    V'(t)=\pi(2r(t)*r'(t)*h(t)+h'(t)r^2(t))

    Consider r(t)=1 and h(t)=2
    Rate of change of the volume : V'(t)=-1 (since it decreases)
    Rate of change of the radius : r'(t)=1.

    (i) Solve for h'(t)
    (ii) same reasoning, with the derivatives. Try to do it.
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