Question

A ball contains 5000 cm³ of air.

More air is pumped into the ball at a rate of 160 cm³ per second.
The ball is full of air when it becomes a sphere with radius 15 cm.

Volume of a sphere = 4/3 pi x r cubed
where r is the radius

Does it take less than 1 minute to fill the ball?
You must show your working.

Answer 1

Yes. it takes 57 seconds.

Explanation:

We first need to calculate the volume of the when it is full of air

volume = 4/3πr³

= 4/3π X 15³

= 14137.17 cm³

we then subtract the amount of air it had before pumping began

that is, 14 137.17 - 5000

= 9137.17 cm³

we need to calculate the time it will take to pump 9137.17 cm³ of air at the rate of 160cm³ per second

1 second = 160 cm³

? = 9137.17 cm³

9137.17/160 = 57.11 seconds

this approximately 57 seconds.

given the fact that 1 minute = 60 seconds, 57 seconds was less than a minute.