Of the spherical segment is given by this formula

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of the spherical segment is given by this formula (which we will assume): V = ( π /3) H (27 – H 2 ). Give EXACT ANSWERS to the questions below. (a) Find the volume of the spherical segment if H=1 $$26 π 3 (b) Find the rate of change of the volume with respect to H of the spherical segment at H=1 : :
(c) Use the tangent line approximation at H=1 to estimate the value of H that will yield a spherical segment having volume 25 cubic inches:
10. 6/6 points | Previous Answers In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles.
12/14/16, 3)58 PM hw18S3.10 According to the ``law of sines,'' you always have: b a = sin B sin A Suppose that a and b are pieces of metal which are hinged at C . At first the angle A is π /4 radians=45 o and the angle B is π /3 radians = 60 o . You then widen A to 46 o , without changing the sides a and b . Our goal in this problem is to use the tangent line approximation to estimate the angle B (a) Notice that the angle B is a function of the angle A ; i.e. B=f(A) . Consequently, it makes sense to calculate the implicit derivative: .
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(c) Write the linear approximation of f at A = π /4:
12/14/16, 3)58 PM hw18S3.10 Page 11 of 11 (d) Using (c), when A = 46 o , B is approximately $$61.732 degrees; either answer exactly or to three decimal places. 11. 2/2 points | Previous Answers A metal rod 1 meter in length is placed horizontally on the x -axis, with its ends located at the points P = (0,0) and Q = (1,0). A second long metal rod is attached to the first one at the point Q =(1,0) and makes an angle of 45 o with the first. A third long metal rod is attached to the first rod at the point P =(0,0) and is free to rotate about P . Thus, the angle θ made by the first and third bars is free to change. For θ between 0 o and 90 o the second and third bars cross at a point R =(x,y) (see figure).

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