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?

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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)"#

#"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"#