[SOLVED] Spherical Balloon - Related Rates Problem 1. The problem statement, all variables and given/known data A spherical balloon is inflated so that its radius increases at a rate of 1 cm/min. How fast is the volume increasing when: a) the diameter is 2000 cm b) the surface area is 324 pi cm^2 ---> I have solved this already 2. Relevant equations V = (4/3)pi(r^3) dV/dt = 4pi(r^2)(dr/dt) 3. The attempt at a solution For part (a) the diameter is 2000 cm. So I make it 1000 cm for Radius Now, I put it in the equation: dV/dt = 4pi(r^2)(dr/dt) where dr/dt = 1cm/min dV/dt = 4pi(1000^2)(1 cm/min) = 4 000 000 pi cm^3 / min But, the answer in the book is 40 000 pi cm^3 / min. Please help me out. Thanks.