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 # 18 #, the cap's height is #4 #, and the cap's radius is #8 #. What is the object's volume?

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Answer 1 · 2017-02-09T09:33:38

The sum of the volume of the prism and the half-sphere.

The volume of the prism:

#l*w*h=V#

#16*16*18 = 4608# cubed units

The volume of the sphere on top:

#4/3pir^3=V# but it is a half sphere, so

#2/3pir^3=V#

#pi2/3*8^3 = 1072# cubed units

Add them together

#1072+4608 = 5680# cubed units