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 #6 #, the cap's height is #4 #, and the cap's radius is #6 #. What is the object's volume?

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Answer 1 · 2018-08-07T14:45:27

1034.96 cu. I would review,for bugs, if any.

From the dimensions of the spherical cap, the semi-angle that it

subtends at the center of its sphere,

#alpha# rad #= arccos ((6-4)/6) = arccos (1/3) = 70.53^o#

# = 1.23 rad#,

The side length of the square top of the prism is

#2 (sqrt( 6^2 - 2^2) ) = 8sqrt2#.

The entire volume = Volume of the cap + volume of the prism

= (( volume of the cone + volume of the

spherical cap ) - volume of the cone) + volume of the prism

#= ( 4/3 (6^3)alpha sin alpha - 1/3 pi ((4sqrt2)^2)(2))#

#+ (6)((8sqrt2)^2#

#= 4/3(6^3) ( 1.23)sqrt( 1 - (1/3)^2 ) - 1/3 pi ((4sqrt2)^2)(2))#

#+ (6)((8sqrt2)^2#

#= 333.98 - 67.02 + 768#

#= 1034.96 cu#