Answer:
answer:
57 in³
Step-by-step explanation:
since the volume of gas and the cube of its radius vary directly, we can set up an initial equation to find the constant of variation:
v = kr³, where v=volume, r=radius and k= contant of variation
given that a balloon with a radius of 3 inches can hold a volume of 81 cubic inches, we can plug these values into the equation and solve for 'k':
81 = k3³ or 81 = 27k or k = 3
given 'k', now we can find the volume of the balloon with a radius of 2:
v = (3)(2³) = 24 in³
since the question asked how much gas must be released to reduce the radius, we would find the difference of 81 and 24:
81 - 24 = 57 in³