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?

1 Answer
Aug 7, 2018

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

Explanation:

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