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

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

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

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

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

$= 333.98 - 67.02 + 768$

$= 1034.96 cu$

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