calculus

A cylinder is generated by rotating a rectangle with perimeter 12 in. about one of its sides.?
Express the volume of the cylinder as a function of x.
Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.

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  1. if the rectangle is rotated about the side with length x, then the height is 6-x.

    v = pi x^2 (6-x) = pi(6x^2 - x^3)
    dv/dx = pi(12x-3x^2) = pi*3x(4-x)

    so, when x=4, v is max.

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  2. A right circular cone of height 24 cm has a curved surface area 550 Square CM it's volume is

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  3. Find the missing dimension of the cylinder. The volume is 28 in3. Round your answer to the nearest whole number.

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