Question
Sarah is blowing up spherical balloons for her brother's birthday party. The balloons have a radius of 2 inches. If she can inflate the balloon at a rate of 150 cubic in. per minute, the time it would take for the balloon to inflate is ___________.
- 0.4 min.
- 1.6 min.
- 2.5 min.
- 0.22 min
Hint:
Here, in this problem, we want to calculate the time taken by Sarah to inflate a spherical balloon whose radius is given. Obviously, the total time required will be the volume of the balloon divided by the rate of inflating the balloon. For this, we have to use the formula for calculating the volume of a sphere. The volume 
of a sphere of radius 
is given by the formula, 
.
The correct answer is: 0.22 min
Given that the radius of the spherical ball is 
inches.
We have to find the volume of the given spherical balloon.
Now, the volume of a spherical balloon of radius is .
So, for inches, we get: 
.
Hence, the volume of the balloon is 
.
Now, the rate of inflating is 
.
So, the time required to inflate the balloon is 
.
Therefore, the time it would take for the balloon to inflate is 
.
Note that, here, we can use 
in the place of 
to find the volume of the given spherical ball using the formula .
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