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 #5 #, the cap's height is #4 #, and the cap's radius is #3 #. What is the object's volume?

1 Answer
Jul 29, 2018

#V=(80pi)/3 + 180#

Explanation:

To find the object's volume, we just need to add the volumes of the #color(red)(spherical)# #color(red)(ca p)# and the #color(blue)(prism)#.

The formula for a #color(red)(spherical)# #color(red)(ca p)# is #color(red)(V)=(pih^2)/3(3r-h)#, where #r# is the radius of the sphere, and #h# is the height of the cap.

Let's plug in the values:

#color(red)(V)=(pi(4)^2)/3(3(3)-(4))#

#color(red)V=color(red)((80pi)/3)#

Next, we find the volume of the #color(blue)(prism)#. The volume of a #color(blue)(prism)# is #color(blue)(V)=bh# where #b# is the area of the base of the prism and #h# is the height of the prism.

Let's plug in the values:

#color(blue)(V)=(6)^2(5)#
#color(blue)(V)=(36)(5)#
#color(blue)(V)=color(blue)(180)#

Now, we add the volume of the spherical cap to the prism to get the final object's volume.

#V=color(red)((80pi)/3) + color(blue)(180)#