THREE submissions are allowed for each question part, except for True/False and

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THREE submissions are allowed for each question part, except for True/False and 2*ftion multiple-choice questions pro We ms. only ONE submission is allowed Exact answers are required unless the question specificity asks for a rot typos oI questions that requite rounded answers display the S*gFig icon beside the answer box Half credrt will be gwe problems only, for answers that are numencalty correct but do not have the correct number of significant >ssw>g operands, incorrect grouping operators, misspelled units, symbols with no response) has been made You wttt not lose submissions for syntax errors Please see the topic. Answenng Math and under the WehAsvgn Student Help System for detaded information and examples Use polar coordinates to find the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 25 and outside the cylinder x^2 + y^2 = 4

Explanation / Answer

Solution:

Solving for z:
x^2 + y^2 + z^2 = 25 ==> z = ± (25 - r^2)
x^2 + y^2 = 4 ==> r = 2.

So, the volume 1 dA equals
( = 0 to 2) (r = 0 to 2) [(25 - r^2) - (-(25 - r^2))] * (r dr d)
= ( = 0 to 2) d * (r = 0 to 2) 2r(25 - r^2)^(1/2) dr
= 2 * (-2/3)(25 - r^2)^(3/2) {for r = 0 to 2}
= (4/3) [125 - 21^(3/2)].

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