Answer:
708π in³ = 2224.25 in.³
Step-by-step explanation:
The composite solid is made up of a cone, a cylinder, and a half sphere.
Recall the volume formulas:
cone: πr²h/3
cylinder: πr²h
sphere: 4πr³/3
half sphere: (1/2) × 4πr³/3
We need to find teh heoght of the cone. The slant height is 10 in. The radius is 6 in. We can use the Pythaogorean theorem to find the height of the cone.
h = √(10² - 6²) = 8
total volume = π(6 in.)²(8 in.)/3 + π(6 in.)²(13 in.) + (1/2) × 4π(6 in.)³/3
total volume = π(96 in.³ + 468 in.³ + 144 in.³)
total volume = 708π in³ = 2224.25 in.³
