An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is # 4 #, the cap's height is #2 #, and the cap's radius is #1 #. What is the object's volume?

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Answer 1 · 2018-04-21T12:31:51

#color(blue)((48+4pi)/3 "cubic units".)#

This is a square prism. The radius of the cap is 1, so the width of the square is 2.

Volume of prism:

Area of base x height.

#2^2xx4=16#

Volume of a spherical cap is given by:

#V=(pih^2)/3(3r-h)#

#V=(pi2^2)/3(3(1)-2)#

#V=(4pi)/3(1)=(4pi)/3#

Total volume:

#16+(4pi)/3=(48+4pi)/3# cubic units.