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 $4$ , and the cap's radius is $3$ . What is the object's volume?

Question

1286 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-12T16:58:42

$color(blue)("Volume"=(1296+80pi)/3 " cubic units")$

This is a square prism. The radius of the cap is 3, so the width of the square is 6.

Volume of prism:

Area of base x height.

$6^2xx12=432$

Volume of a spherical cap is given by:

$V=(pih^2)/3(3r-h)$

$V=(pi(4)^2)/3(3(3)-4)$

$V=(16pi)/3(5)=(80pi)/3$

Total volume:

$432+(80pi)/3=(1296+80pi)/3$ 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 4 4 , and the cap's radius is 3 3 . What is the object's volume?