# 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

#### 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

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:

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:

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

Plug everything in and we get:

Add the two volumes together for your answer: