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 # 3 #, the cap's height is #7 #, and the cap's radius is #8 #. What is the object's volume?
1 Answer
Explanation:
I use the formula:
Volume of the cone-ice like part of a sphere of radius a
where
cone, from the center of the sphere to the periphery of the cap.
From the dimensions of the opposite spherical cap,
the semi-angle that this opposite cap subtends at the center of
its sphere,
Here,
The side length of the square-top of the prism is
The entire volume
V = volume of the opposite spherical
cap + volume of the rectangular cylinder below
The volume of the spherical cap
= the volume of the con-
ice-like part of the sphere that has this cap as its top - volume of
the cone part. Now,