We are given that a spherical balloon has a radius of 3 inches. We are asked to find the volume of the balloon. Let's start by drawing it.
To find the volume of the balloon, recall that the volume of a sphere is equal to four thirds the product of π and the cube of the radius r.
V=4/3Ï€ r^3
In this case, the radius of the sphere is 3 inches. We can substitute the radius into the formula. Then, we will simplify the right-hand side to get the volume of the sphere. Let's do it!
We got that the volume of the balloon is about 113.1 cubic inches.
We are asked to find how long it will take Sarah to inflate the balloon.
We know that she can inflate the balloon at a rate of 200 cubic inches per minute. Moreover, in Part A, we got that the volume of the balloon is about 113.1 cubic inches. Let's use these facts to write a proportion that will help us to find the balloon inflation time.
&200in^3/1min=113.1in^3/xmin
Now that the proportion is written, we will solve it using cross products and then isolating x.
