Question
A spherical ball has a radius of 2 inches. The ball has a slow leak which the air escapes at a rate of 1 cubic inches per second. The time it would take for the ball to deflate is ___________.
- 10.6 s
- 41 s
- 33.5 s
- 14.2 s
Hint:
Here, in this problem, we want to calculate the time required to deflate the spherical ball whose radius is given. Obviously, the total time required will be the volume of the air inside the ball divided by the rate of escaping of the air through the leak from the ball. Now, the total volume of air inside the ball is the same as the volume of the given spherical ball. 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: 33.5 s
Given that the radius of the spherical ball is 
inches.
We have to find the total volume of the air inside the ball. Now, the volume of the air will be the same as the volume of the spherical ball. Now, the volume of a spherical ball of radius is .
So, for inches, we get: 
.
Hence, the volume of the air is 
.
Now, the rate at which the air is escaping through a slow leak is 
.
So, the time required to deflate the ball is 
.
Therefore, the time it would take for the ball to deflate is 
.
Note that, here, we can use 
in the place of 
to find the volume of the given spherical ball using the formula .
Related Questions to study
If a tennis ball has a diameter of 7, find the volume of the tennis ball. Use 3.14 for pi. Round to the nearest whole number (the ones place).
Note that the value of is taken as 
which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as 
also.
If a tennis ball has a diameter of 7, find the volume of the tennis ball. Use 3.14 for pi. Round to the nearest whole number (the ones place).
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 4.1 cm.
Note that, we can use in the place of to find the volume of the given sphere using the formula 
.
Find the volume of a sphere with the radius of 4.1 cm.
Note that, we can use in the place of to find the volume of the given sphere using the formula .
Find the volume of a sphere with the radius of 1 inches.
Note that, here, we can substitute 
to find the volume of the given sphere using the formula .
Find the volume of a sphere with the radius of 1 inches.
Note that, here, we can substitute to find the volume of the given sphere using the formula .
Annette wanted to know how much ice cream she got in one scoop. The radius of a scoop is 1.4 inches. Find the volume. Use 3.14 for pi.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Annette wanted to know how much ice cream she got in one scoop. The radius of a scoop is 1.4 inches. Find the volume. Use 3.14 for pi.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 14 inches.
Here, we can substitute 
to find the volume of the given sphere using the formula .
Find the volume of a sphere with the radius of 14 inches.
Here, we can substitute to find the volume of the given sphere using the formula .
The half of a sphere is called ___________
The half of a sphere is called ___________
Find the volume of a sphere with the radius of 2.6 cm.
Here, in this problem, we can substitute in the formula to find the volume of the given sphere.
Find the volume of a sphere with the radius of 2.6 cm.
Here, in this problem, we can substitute in the formula to find the volume of the given sphere.
Find the volume of a sphere with the radius of 3.2 inches.
Here, to find the volume of the sphere using the formula , we can substitute the value of as or .
Find the volume of a sphere with the radius of 3.2 inches.
Here, to find the volume of the sphere using the formula , we can substitute the value of as or .
Jack wants to know how much water a sphere can hold with a radius of 8 cm. Find the volume. Use 3.14 for pi.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Jack wants to know how much water a sphere can hold with a radius of 8 cm. Find the volume. Use 3.14 for pi.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 1.5 inches.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 1.5 inches.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 1.9 cm.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 1.9 cm.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 2 inches.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 2 inches.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 4 inches.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
Find the volume of a sphere with the radius of 4 inches.
Note that the value of is taken as which is an approximate value of . Though it is not exact, we can use this to find the value of a mathematical expression. We can take the value of as also.
