Answer:
The radius increase when the volleyball is fully inflated is 0.5
Step-by-step explanation:
Volume of Partially inflated volleyball = 180 in³
Volume of Full inflated volleyball = 294 in³
We need to find how much does the radius increase when the volleyball is fully inflated?
First we will find the radius of both Partially inflated and Full inflated volleyball. Then we will find increase in radius.
The formula for Volume of sphere is: [tex]Volume=\frac{4}{3}\pi r^3[/tex]
Finding Radius of Partially inflated volleyball
Volume = 180
Putting values and finding radius of Partially inflated volleyball
[tex]Volume=\frac{4}{3}\pi r^3\\180=\frac{4}{3}*3.14*r^3\\4.186r^3=180\\r^3=\frac{180}{4.186}\\r^3=43.0\\Taking\:cube\:root\:on\:both\:sides\\\sqrt[3]{r^3}=\sqrt[3]{47}\\r= 3.6[/tex]
So, radius of Partially inflated volleyball is r = 3.6
Finding Radius of Fully inflated volleyball
Volume = 294
Putting values and finding radius of Fully inflated volleyball
[tex]Volume=\frac{4}{3}\pi r^3\\294=\frac{4}{3}*3.14*r^3\\4.186\:r^3=294\\r^3=\frac{294}{4.186}\\r^3=70.23\\Taking\:cube\:root\:on\:both\:sides\\\sqrt[3]{r^3}=\sqrt[3]{70.23}\\r= 4.1[/tex]
So, radius of Partially inflated volleyball is r = 4.1
Now, finding increase in radius by subtracting radius of fully inflated volleyball with partially inflated volleyball
Increase in radius of Fully inflated volleyball = 4.1 - 3.6
Increase in radius of Fully inflated volleyball = 0.5
So, the radius increase when the volleyball is fully inflated is 0.5
