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Problem Set
- Problem 1: Find the volume of a sphere with radius = 9 ext{ cm}$.
- Problem 2: A spherical balloon has diameter = 30 ext{ cm}$. Find its volume in liters.
- Problem 3: A ball has volume = 288\pi ext{ cm}^3$. What is its diameter?
- Problem 4: If the radius of a sphere is doubled, by what factor does its volume increase?
Solutions and Explanations
- Solution 1: = ⁴⁄₃\pi(9)^3 = ⁴⁄₃\pi(729) = 972\pi \approx \mathbf{3,053.63 ext{ cm}^3}$.
- Solution 2: = 15 ext{ cm}$, = ⁴⁄₃\pi(15)^3 = 4500\pi \approx 14,137.17 ext{ cm}^3 = \mathbf{14.14 ext{ Liters}}$.
- Solution 3: \pi r^3 = 288\pi \implies r^3 = (288 imes 3)/4 = 216 \implies r = 6 ext{ cm} \implies d = \mathbf{12 ext{ cm}}$.
- Solution 4: Volume increases by a factor of $2^3 = \mathbf{8}$.