Question

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 `8`, and the cap's radius is `4`. What is the object's volume?

Answer 1

`color(purple)("Volume of the object " V_o = 512 + (256/3) pi ~~ color(chocolate)(780.08 " cubic units"`

Explanation:

`"Prism's height " H_p = 12, " Radius of sphere " R_c = 4, " Height of cap " H_c = 8 = D_c = 2 * R_c`

It's a sphere over square prism with side of square base and the diameter of sphere same. i.e. `S_p = D_c = 8`

`"Volume of prism " V_p = S_p^2 * H_p = 8*2 * 12 = 512`

`"Volume of sphere " V_s = 4/3 pi R_c^3 = 4/3 * pi * 4^3 = (256/3) pi`

`"Volume of the object " V_o = V_p + V_s = 512 + (256/3) pi ~~ 780.08 " cubic units"`