Function notation example

Frank wants to fill up a spherical water balloon with as much water as possible the balloons he bought can stretch to a radius of three inches not too big if the Ballu if the volume of a sphere is and this is volume as a function of radius is equal to 4/3 PI R cubed what volume of water in cubic inches can Frank put into the balloon so this function definition is going if you give it a radius in inches it's going to produce a volume in cubic inches so let's rewrite it volume as a function of radius is equal to 4/3 PI R cubed now they say the balloons he bought can stretch to a radius of 3 inches so let's think about if the radius gets to 3 inches what the volume of that balloon is going to be so we essentially would just input 3 inches into our function definition so everywhere where we see in R we would replace it with a 3 so we could write it just to be clear let me rewrite it in the same color V of that's not the same color we do it in that brownish brownish color right over here so V of 3 V of 3 is equal to is equal to 4/3 pi instead of R cubed I would write 3 cubed 3 4/3 PI 3 cubed 3 cubed this is how the function definition works whatever we input here it will replace the R in the expression so V of 3 is going to be equal to so this is going to be equal to 4/3 pi times 3 to the third power is 27 27 divided by 3 is 9 so this is 9 9 times 4 is 36 PI so this is equal to 36 pi and since this was in inches our volume is going to be in inches in inches in inches cubed or cubic inches so that's the volume of water that Frank can put in the balloon 36 PI cubic inches you