a circle is inscribed in a square. the circumference of the circle is increading at a constant rate of 6 inches per second. As the circle ex

Question

a circle is inscribed in a square. the circumference of the circle is increading at a constant rate of 6 inches per second. As the circle expands, the aquare expands to maintain the condition of tangency. find th rate at which the perimeter of the square is increasing

in progress 0
Madeline 2 months 2021-09-25T06:36:05+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-25T06:37:37+00:00

    Answer:

    The rate at which Perimeter of the square is increasing is \frac{24}{\pi} \ in/secs.

    Step-by-step explanation:

    Given:

    Circumference of the circle = 2\pi r

    Rate of change of in circumference = 6 in/secs

    We need to find the rate at which the perimeter of the square is increasing

    Solution:

    Now we know that;

    \frac{d(2\pi r)}{dt} =6\\\\2\pi\frac{dr}{dt}=6\\\\\frac{dr}{dt}=\frac{6}{2\pi}\\\\\frac{dr}{dt}=\frac{3}{\pi}

    Now we know that;

    side of the square= diameter of the circle

    side of the square = 2r

    Now Perimeter of the square is given by 4 times length of the side.

    P=4\times 2r =8r

    Now we need to find the rate at which Perimeter is increasing so we will find the derivative of perimeter.

    \frac{dP}{dt}= \frac{d(8r)}{dt}\\\\\frac{dP}{dt}= 8\times\frac{dr}{dt}

    But \frac{dr}{dt} =\frac{3}{\pi}

    So we get;

    \frac{dP}{dt}= 8\times\frac{3}{\pi}\\\\\frac{dP}{dt}= \frac{24}{\pi}\  in/sec

    Hence The rate at which Perimeter of the square is increasing is \frac{24}{\pi} \ in/secs.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )