DC/AC=EC/BC
x/(x+3)=10/16
10(x+3)=16x
10x+30=16x
30=6x
x=5
DC=x=5
DC=5 units long
10/16=DE/AB, DE=y
10/16=y/10
16*y=10*10
y=6.25≈6.3
DE≈6.3
Triangles with height
and base
, with
have area
.
Such cross sections with the base of the triangle in the disk
(a disk with radius 5) have base with length

i.e. the vertical (in the
plane) distance between the top and bottom curves describing the circle
.
So when
, the cross section at that point has base

so that the area of the cross section would be 6^2/2 = 18.
In case it's relevant, the entire solid would have volume given by the integral

Since 3 squared is 9 and 4 squared is 16, the square root of 13 will fall somewhere between 3 and 4