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 $7$ , the cap's height is $8$ , and the cap's radius is $8$ . What is the object's volume?

Question

3912 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-20T01:22:40

$color(maroon)("Volume of the object " = pi r^2 H + (2/3) pi r^3 ~~ 2479.7638 " cubic units"$

$"Volume of the object " = " Volume of cylindrical prism + Volume of spherical cap (or hemisphere)"$

![https://www.tes.com/lessons/y-o0ZGceDbjvUA/copy-of-volume-cylinders-cones-and-spheres](useruploads.socratic.org)

$"Vol. of Spherical Cap " V_s = (2/3) pi r^3 " as " r = h$

$"Volume of Prism = V_p = pi r^2 H$

$"Given ' r = 8, H = 7$

$"Vol. of object " V_o = V_p + V_s$

$V_o = pi ^ 8^2 * 7 + (2/3) * pi * 8^3$

$color(maroon)(V_o = pi * 8^2 * ( 7 + 16/3) ~~ 2479.7638 " cubic units"$

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 7 7 , the cap's height is 8 8 , and the cap's radius is 8 8 . What is the object's volume?