BIf the balloon is half-inflated, it means that its volume is half the the volume of a fully inflated balloon.
CSubstitute the volume found in Part B into the formula for the volume of a sphere. Then solve the resulting equation for the radius.
A5324Ï€/3 in.^3
B2662Ï€/3 in.^3
Cabout 8.7 in.
Practice makes perfect
We are told that q sphere-shaped balloon has a diameter of 22 inches when fully inflated.
We want to find its volume. Recall that the volume of a sphere is four thirds the product of π and the cube of the radius.
V=4/3Ï€ r^3
From the diagram we can see that the diameter is 22 inches. This means that the radius is 22÷ 2=11 inches. We can substitute this value for r into the formula and simplify the right-hand side.
The volume of the fully inflated balloon is 5324Ï€3 cubic inches.
Half of the air is let out of the balloon. We want to find its new volume V_2, assuming that the balloon remains a sphere. Remember the initial volume V_1 found in Part A.
V_1=5324Ï€/3
Since half of the air was let out of the balloon, the volume is now twice as small, or half as much, as it was before. Let's calculate the new volume V_2.
The volume of the half-inflated balloon is 2662Ï€3 cubic inches.
We previously found the volume of a half-inflated balloon.
2662Ï€/3 in.^3
We are asked to find its radius. To do so, we substitute 2662Ï€3 for V in the formula for the volume of a sphere. Then we will solve for r. Let's do it!
