SOLUTION: calculate and compare the volume of three pairs of spheres with the following radii. pair 1 (r =1', r=2') pair 2 (r = 3', r', = 6') pair 3 (r=4',r=8') What happens to the volum

Question 117579: calculate and compare the volume of three pairs of spheres with the following radii.
pair 1 (r =1', r=2') pair 2 (r = 3', r', = 6') pair 3 (r=4',r=8')
What happens to the volume of a sphere if its radius is doubled? Why?
thank you
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The volume of a sphere (V) can be calculated using the equation:
.

.
in which R represents the radius of the sphere. If you multiply out the constants:
.

.
you get a product 4.18879025 and substituting this product into the volume equation simplifies
it to:
.

.
Using this form of the equation, all you have to do for this problem is enter the constant 4.18879025
into your calculator's memory. Then for each of the given spheres, cube its radius and
multiply that by the constant which you can recall from memory.
.
For example. The first pair ... one sphere has a radius of 1 ft. Cube that to get 1 cu ft
and multiply that by 4.18879025 to get an answer of 4.18879025 cu ft.
.
The first pair ... second sphere has a radius of 2 ft. Cube that and you get 8 cu ft. Then
multiply that by 4.18879025 and you get the volume to be 33.51032164 cu ft.
.
It may be apparent to you now that when you doubled the radius the volume went up 8 times.
That is because the cube of R is and the cube of 2R is .
The ratio of these two is .
.
You can now apply this same technique to the remaining 2 pairs of spheres. When you do, you
should get the following answers:
.
Pair 2. The sphere with the radius of 3 ft has a volume of cu ft
and the sphere with the radius of 6 ft has a volume of cu ft
.
Pair 3. The sphere with the radius of 4 ft has a volume of cu ft
and the sphere with the radius of 8 ft has a volume of cu ft
.
In each pair, if you take divide the answer for the volume of the first sphere into the answer
for the volume of the second sphere you should get an answer of 8.
.
Hope this helps you to understand the problem and how you can work it.
.
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