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 # 10 #, the cap's height is #7 #, and the cap's radius is #8 #. What is the object's volume?

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Answer 1 · 2018-04-20T13:05:36

#color(blue)((833pi+7680)/3" cubic units.")#

This is a square prism. The radius of the cap is 8, so the width of the square is 16.

Volume of prism:

Area of base x height.

#16^2xx10=2560#

Volume of a spherical cap is given by:

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

#V=(pi7^2)/3(3(8)-7)#

#V=(pi49)/3(17)=(833pi)/3#

Total volume:

#(833pi)/3+2560=(833pi+7680)/3# cubic units.