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

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Answer 1 · 2018-08-11T10:11:41

$color(purple)("Volume of the object " V_o = 512 + (256/3) pi ~~ color(chocolate)(780.08 " cubic units"$

$"Prism's height " H_p = 12, " Radius of sphere " R_c = 4, " Height of cap " H_c = 8 = D_c = 2 * R_c$

It's a sphere over square prism with side of square base and the diameter of sphere same. i.e. $S_p = D_c = 8$

![http://nickcassway.com/designblog/?p=1190]( useruploads.socratic.org )

$"Volume of prism " V_p = S_p^2 * H_p = 8*2 * 12 = 512$

$"Volume of sphere " V_s = 4/3 pi R_c^3 = 4/3 * pi * 4^3 = (256/3) pi$

$"Volume of the object " V_o = V_p + V_s = 512 + (256/3) pi ~~ 780.08 " cubic units"$

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 lengths of the top. The prism's height is 12 12 , the cap's height is 8 8 , and the cap's radius is 4 4 . What is the object's volume?