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

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