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:

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

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