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 # 16 #, the cap's height is #1 #, and the cap's radius is #5 #. What is the object's volume?

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Answer 1 · 2018-06-13T19:45:24

#color(blue)("Volume"=(4800+14pi)/3 " cubic units")#

This is a square prism. The radius of the cap is 5, so the width of the square is 10.

Volume of prism:

Area of base x height.

#10^2xx16=1600#

Volume of a spherical cap is given by:

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

#V=(pi(1)^2)/3(3(5)-1)#

#V=(14pi)/3#

Total volume:

#1600+(14pi)/3=(4800+14pi)/3# cubic units.