Question

PLEASE HELP!!!!! I NEED THIS FAST!!!!!!

An environmental equipment supplier sells hemispherical holding ponds for treatment of chemical waste. The volume of a pond is V1=1/2(3/4πr1^3), where r1 is the radius in feet. The supplier also sells cylindrical collecting tanks. A collecting tank fills completely and then drains completely to fill the empty pond. The volume of the tank is V2=12πr2^2, where r2 is the radius of the tank.

a. Since v1=v2, write an equation that shows r1 as a function of r2. Write an equation that shows r2 as a function of r1.

b. You want to double the radius of the pond. How will the radius of the tank change?

Answer 1

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