At the bottom of the composite figure we have half a sphere, of radius 10 in.
The volume of this hemisphere would be half the volume of the full sphere, or:
(1/2)(4/3)π(10 in)^3, or (2/3)π(1000 in^3), or (2000/3)π in^3.
On top is the cone of radius 10 and slant height 15 in. To find the volume of this cone-shaped solid, we'll need the height of the cone. This can be found using the Pyth. Thm. as follows:
15^2 = 10^2 + h^2, where h is the height of the cone.
225 = 100 + h^2, so that h= √125, or 5√5. The height of the cone is 5√5 in.
Then the volume of the cone is V = (1/3)(base)(height)
= (1/3)(π)(100 in^2)(5√5 in)
= 500√5/3(π) in^3
The total volume of the composite solid is then
(2000/3)(π in^3) + ( 500√5/3(π) ) in^3), or
(π/3)(4+√5) in^3. This comes out to 6.53 in^3, to the nearest hundredth.
