A spherical balloon has a 14-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere.
A.find the volume of the fully inflated balloon.
B.find the volume of the half inflated balloon.
C.what is the radius of the half inflated balloon?
A. The diameter of the fully inflated balloon is 14 inches, so the radius is 7 inches. The formula for the volume of a sphere is V = (4/3)πr³. Plugging in the radius gives:
V = (4/3)π(7³) = 1436.76 cubic inches
Therefore, the volume of the fully inflated balloon is approximately 1436.76 cubic inches.
B. If half of the air is let out of the balloon, the volume will be reduced by half. That means the volume of the half inflated balloon is:
V/2 = (1436.76 cubic inches)/2 = 718.38 cubic inches
Therefore, the volume of the half inflated balloon is approximately 718.38 cubic inches.
C. The formula for the volume of a sphere can also be rearranged to solve for the radius:
V = (4/3)πr³
r³ = (3V)/(4π)
r = (3V/(4π))^(1/3)
Using the volume of the half inflated balloon from part B:
r = (3(718.38 cubic inches)/(4π))^(1/3) ≈ 5.070 inches
Therefore, the radius of the half inflated balloon is approximately 5.070 inches.