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Problem 1: Basketball Air Capacity
Scenario: A regulation basketball has a circumference of 75 cm. How many cubic centimeters of air does it hold?
- Find radius: = C / (2\pi) = 75 / (2 imes 3.14159) \approx 11.9366 ext{ cm}$.
- Calculate volume: = ⁴⁄₃ imes \pi imes (11.9366)^3 \approx ⁴⁄₃ imes \pi imes 1700.74 \approx \mathbf{7,124.7 ext{ cm}^3}$.
Problem 2: Melting Spherical Ice Ball
Scenario: A cocktail ice ball has diameter 6 cm. If it melts into a cylindrical glass of diameter 8 cm, what will the liquid water height be?
- Ice volume: = ¹⁄₆\pi(6)^3 = 36\pi ext{ cm}^3 \approx 113.10 ext{ cm}^3$.
- Glass base area: = \pi(d/2)^2 = \pi(4)^2 = 16\pi ext{ cm}^2$.
- Water height: = V / A = (36\pi) / (16\pi) = 36/16 = \mathbf{2.25 ext{ cm}}$.