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The area of a circle is given by A=pir^(...

The area of a circle is given by `A=pir^(2)`, where r is the radius . Calculate the rate of increases of area w.r.t. radius.

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The correct Answer is:
`2pir`
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The area of a circle is given by A= pi r^(2) , where r is the radius. Calculate the rate of increase of area w.r.t radius.

Area of a circle = 2pir^(2) .

Knowledge Check

  • The diameter of a circle is increasing at the rate of 1 cm/sec. When its radius is pi , the rate of increase of its area, is

    A
    `pi cm^(2)//sec`
    B
    `2 pi cm^(2)//sec`
    C
    `pi^(2) cm^(2)//sec`
    D
    `2pi^(2) cm^(2)//sec`

  • The volume of a sphere is given by V=4/3 piR^(3) where R is the radius of the radius of the sphere. Find the change in volume of the sphere as the radius is increased from 10.0 cm to 10.1 cm . Assume that the rate does not appreciably change between R=10.0 cm to R=10.1 cm

    A
    `10 pi cm^(3)`
    B
    `20 pi cm^(3)`
    C
    `30 pi cm^(3)`
    D
    `40 pi cm^(3)`

  • If the radius of a circle is 2 cm and is increasing at the rate of 0.5 cm/sec., then the rate of increase of its area is

    A
    `pi cm^(2)//sec`
    B
    `2pi cm^(2)//sec`
    C
    `3pi cm^(2)//sec`
    D
    `4pi cm^(2)//sec`

    • Similar Questions

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    If the rate of increase of the radius of a circle is 5 cm/sec, then the rate of increase of its area, when the radius is 20 cm, will be

    If the radius of a circle increases at a uniform rate of 2 cm//s , then the rate of increase of area of circle, at the instant when the radius is 20 cm, is

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