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

1 Answer
May 26, 2017

V ~~ 3200.76

Explanation:

We want to do this in two parts, the sphere and the prism.

We know the diameter is equal to the length of the top, and we know that d=2r

In doing this we determine the diameter to be 14, as the radius is 7.

Now let's start with the prism's volume. The volume of a prism is:

V = lwh

Since the top is a square, length and width are the same, 14 (the diameter of the cap). So we plug everything in to get:

V = 14^2*9
V = 1764

Now the sphere part. The volume of a sphere is:

V = 4/3pir^3 But since we are dealing with half a sphere, we will use this:
V = 2/3pir^3

Plug everything in and we get:

V = 2/3pi(7)^3
V = 1372pi/3

Add the two volumes together for your answer:

1372pi/3+1764 = V
V ~~ 3200.76