Question #c1f8f

2 Answers
Alan P.
Sep 8, 2017

Volume of bounded area #=color(red)(9pi)# cubic units

Explanation:

First let's consider this within the XY-plane
#y=sqrt(9-x^2)#
is the equation for the top half (since the root symbol restricts us to non-negative vales) of a circle with center the origin and radius #sqrt(9)=3#
bounding this by #y=0# and #x=0#
implies we are dealing (within the XY-plane) with a quarter circle (whose radius is #3# units)

If we rotate this about the X-axis we will obtain half of a sphere.

The volume of a sphere is #V=4/3pir^3#

Here the radius, #r=3#, and we only want half of the sphere.

So
#color(white)("XXX")"Volume"_"bound region"=1/2 xx 4/3pi xx3^3#

#color(white)("XXX")=9pi# (cubic units)

Frederico Guizini S.
Sep 26, 2017

I have solved this way:

Explanation:

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