Who says V1=V2? if we simplify we get (2/3)pir₁³=12pir₂² for V1 to equal V2
a. solve for r₁ to find r₁ as a function of r₂ (2/3)pir₁³=12pir₂² times 3/2 both sides and divide by pi r₁³=18r₂² cube root both sides r₁=∛(18r₂²)
if solve for r₂ (2/3)pir₁³=12pir₂² divide by 12pi both sides (1/18)r₁³=r₂² squer root both sides √((1/18)r₁³)=r₂
double radius of pond which is r1 √((1/18)r₁³)=r₂ r₁ turns to 2r₁ to double radius √((1/18)(2r₁)³)=r₂double √(8(1/18)(r₁)³)=r₂double (√8)(√((1/18)(r₁)³))=r₂double √((1/18)r₁³)=r₂ so (√8)(r₂)=r₂double (2√2)(r₂)=r₂double the radius of the tank is multipled by 2√2
