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 lengths of the top. The prism's height is # 12 #, the cap's height is #4 #, and the cap's radius is #3 #. What is the object's volume?

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Answer 1 · 2018-06-12T16:58:42

#color(blue)("Volume"=(1296+80pi)/3 " cubic units")#

This is a square prism. The radius of the cap is 3, so the width of the square is 6.

Volume of prism:

Area of base x height.

#6^2xx12=432#

Volume of a spherical cap is given by:

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

#V=(pi(4)^2)/3(3(3)-4)#

#V=(16pi)/3(5)=(80pi)/3#

Total volume:

#432+(80pi)/3=(1296+80pi)/3# cubic units.