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
to get the x coordinate increment
we subtract x coordinate D from F and would be (-6.5) - (-8.25)=1.75 and then divide it by two to get the increment of one step and that would be 1.75 / 2 =0.875
now we get the y coordinate increment
we subtract y coordinate D from F and would be (-7.5) - (-5.75)=-1.75 and then divide it by two to get the increment of one step and that would be -1.75 / 2 =-0.875
A = (D x coordinate - 1.75,D y coordinate +1.75) A=(-10,-4)
I = (H x coordinate + 0.875,d H coordinate -0.875)
I=(-3.875,-10.125)
4,750 divided by 25 = 190, so 190 centimeters wide.
