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 length of the top. The prism's height is $16$ , the cap's height is $1$ , and the cap's radius is $5$ . What is the object's volume?

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Answer 1 · 2018-06-13T19:45:24

$color(blue)("Volume"=(4800+14pi)/3 " cubic units")$

This is a square prism. The radius of the cap is 5, so the width of the square is 10.

Volume of prism:

Area of base x height.

$10^2xx16=1600$

Volume of a spherical cap is given by:

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

$V=(pi(1)^2)/3(3(5)-1)$

$V=(14pi)/3$

Total volume:

$1600+(14pi)/3=(4800+14pi)/3$ 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 length of the top. The prism's height is 16 16 , the cap's height is 1 1 , and the cap's radius is 5 5 . What is the object's volume?