The volume of the cake is 1470 in³.
volume of a cylinder = πr² x height
(Think about how a cylinder is basically a bunch of circles stacked on top of each other. To find the volume, first you need the area of the circle (πr², then you multiply by how many circles you are stacking on top of each other (height))
we know the diameter of the cylinder is 12 in. and the radius is half of the diameter.
half of 12 is 6, therefore the radius is 6 in. or r = 6
Assuming pi is 3.14, solve for the height of the cylinder
1470 = (3.14)(6²)(height)
1470 = 3.14 x 36 x height
1470 = 113.04 x height
height ≈ 13 in
Now that we know the height of the cylinder is about 13 in., we know the height of the cone, because the problem says that the height of the cone is half the height of the cylinder.
half of 13 is 6.5, therefore the height of the cone is 6.5
the radius of the cone is the same as that of the cylinder, 6 in.
volume of a cone = πr² × (height ÷ 3)
volume of the cone = (3.14)(6²)(6.5 ÷ 3)
volume of the cone = (3.14)(36)(2.16666)
volume of the cone = 244.92 in³
Now all that's left to find the volume of the whole cake is to add the volume of the cylinder to the volume of the cone.
1470 + 244.92 = 1714.92 in³
