Final answer:
The approximate absolute difference in the volumes of a baseball and a basketball, with radii of 1.47 inches and 4.61 inches respectively, is 367.55 cubic inches.
Step-by-step explanation:
To calculate the approximate absolute difference in the volumes of the baseball and basketball, we first need to find the volume of each using the formula V = (4/3)πr³, where V is the volume and r is the radius of the sphere.
For the baseball with a radius of 1.47 inches, the volume (Vbaseball) is calculated as follows:
Vbaseball = (4/3)π(1.47 inches)³
Vbaseball = (4/3) × 3.14 × (1.47 inches)³
Vbaseball = (4/3) × 3.14 × 3.18 inches³
Vbaseball = 42.41 inches³
For the basketball with a radius of 4.61 inches, the volume (V basketball) is calculated as follows:
Vbasketball = (4/3)π(4.61 inches)³
Vbasketball = (4/3) × 3.14 × (4.61 inches)³
Vbasketball = (4/3) × 3.14 × 97.77 inches³
Vbasketball = 409.96 inches³
The absolute difference in their volumes, ΔV, is then:
ΔV = V basketball - Vbaseball
ΔV = 409.96 inches³ - 42.41 inches³
ΔV = 367.55 inches³
Therefore, the approximate absolute difference in the volumes of baseball and basketball is 367.55 cubic inches.