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?

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Answer 1 · 2017-05-26T02:36:49

#V ~~ 3200.76#

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#