You measure the salt water in the tank to have a density of 1.02 g/mL. The balloon weighs 2.0 g and your weights have a mass of 30.0 g each. If you put 4 weights in your balloon, you must inflate the balloon to what diameter for it to have a density equal to the salt water, and therefore float in the middle of the tank?
Hint: Set the Volume of the Balloon equal to the equation for the volume of a sphere and solve for the diameter. V = 4/3(pi)(r)^3 and D= 2*r

Question

You measure the salt water in the tank to have a density of 1.02 g/mL. The balloon weighs 2.0 g and your weights have a mass of 30.0 g each. If you put 4 weights in your balloon, you must inflate the balloon to what diameter for it to have a density equal to the salt water, and therefore float in the middle of the tank? 
Hint: Set the Volume of the Balloon equal to the equation for the volume of a sphere and solve for the diameter. V = 4/3(pi)(r)^3 and D= 2*r

aaronq · Answer

if the total mass is, 2.0 g + (4)(30.0 g)= 122.0 g  and you need a density of 1.02 g/mL, then you need a volume of:

     $\rho=\dfrac{m}{V}\rightarrow 1.02\;g/mL=\dfrac{122.0\;g}{V}\rightarrow V=1.02\;g/mL*122.0 g$

                           once you find the volume, plug into:

                                $V = \dfrac{4}{3}\pi*(r)^3 =\dfrac{4}{3}\pi*(\dfrac{d}{2})^3 $

                                           solve for d (diameter).

anonymous · Answer

I have a question about this, For Volume it says 1.02g/mL * 122.0g 
do you multiple or divide it? "1.02g/mL / 122.0g" since v=m/d

aaronq · Answer

oh you divide, sorry i wrote that incorrectly! thanks for the correction