We are asked to find how long it would take the ball to deflate. Let's start by calculating the volume of the ball. To do so, 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^3In this case, we are given the diameter of the sphere. To find the radius, we can divide the diameter d by 2.
Therefore, the volume of the ball is about 268.1 cubic inches. We also know that the ball has a slow leak in which the air escapes at the rate of 2.5 cubic inches per second. This means that we can use a proportion to find how long it would take the ball to deflate. Let's write the proportion!
&2.5in^3/1sec=268.1in^3/xsec
Now that the proportion is written, we will solve it using cross products and then isolating x.
