Final answer:
To find the volume of a spherical cone, we need to find the volume of the sphere and subtract the volume of the cone. Using the given values, the volume of the spherical cone is approximately 50684.79 cm³.
Step-by-step explanation:
To find the volume of a spherical cone, we first need to find the volume of the sphere and then subtract the volume of the cone.
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.
So, the volume of the sphere with radius 17cm is V = (4/3)π(17³) = 16304π cm³.
Next, we need to find the volume of the cone. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the base of the cone and h is the height of the cone.
In this case, the radius of the cone is 8cm and the height is also 8cm, since it stretches from the center of the sphere to the edge of the sphere.
So, the volume of the cone is V = (1/3)π(8²)(8) = 170.67π cm³.
Finally, we can find the volume of the spherical cone by subtracting the volume of the cone from the volume of the sphere: V = 16304π - 170.67π = 16133.33π cm³.
Now, we can approximate the value of π as 3.14 and calculate the volume of the spherical cone: V ≈ 16133.33(3.14) = 50684.79 cm³.
Therefore, the volume of the spherical cone in the sphere is approximately 50684.79 cm³. None of the given options (A, B, C, D) match this value, so none of them are correct.