Question

Find the volume of the composite figure. Explain your thought, explain how your arrived at your answer. SHOW YOUR WORK FOR FULL CREDIT!

Answer 1

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.