Final answer:
To find the volume and surface area of the object, calculate the volume and outer surface area of the sphere, then subtract the volume of the cylindrical hole. The volume of the hole-drilled sphere is approximately 56209.3752 cm³, and the outer surface area is approximately 7238.2296 cm².
Step-by-step explanation:
To calculate the volume and outer surface area of the spherical object with a hole drilled through its center, we need to use the given formulae for a sphere. The drill creates a cylindrical hole, so the volume of that cylinder will have to be subtracted from the volume of the sphere.
(a) Volume of the object:
The formula to calculate the volume of a sphere is V = 4/3 π r³. So, for a sphere of radius 24 cm, the volume is:
V = 4/3 π (24 cm)³ = 57905.8352 cm³ approximately.
However, we must subtract the volume of the cylindrical hole drilled through the center. The volume of a cylinder is given by V = π r² h, where h equals the diameter of the sphere. So, the volume of the cylinder is:
V = π (3 cm)² (2 × 24 cm) = 1696.46 cm³ approximately.
The volume of the spherical object after drilling the hole is the volume of the sphere minus the volume of the cylinder:
Volume of object with hole = 57905.8352 cm³ - 1696.46 cm³ = 56209.3752 cm³ approximately.
(b) Outer Surface Area of the object:
The surface area of a sphere is given by A = 4 π r². Thus, the outer surface area of the sphere of radius 24 cm is:
A = 4 π (24 cm)² = 7238.2296 cm² approximately.