Question 157622: I have a sphere with a diameter of 88,846 miles, and another sphere with a diameter of 7,926 miles. how would i find the surface area to compare, and then eventually find the ratio between the surface areas?
then, using the same numbers, i need to find the ratio of their volumes?
which means i need to know how to find their volumes.
i know the formula for surface area is SA=4(3.14159)r^2
or surface area=four times pi times the radius squared.
then the volume formula would be volume=4/3 times pi times radius cubed (^3)
i dont know if this makes ANY sense... but i dont understand why everytime i calculate such big numbers on my calculator, it says something about "E+11" at the end.. i dont understand it.
HELP?
:)thanks.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! .
Note: E+11 is exponential notation for 10^11 (that's eleven zeros)
.
Let's take it one step at a time:
how would i find the surface area to compare?
SA=4(3.14159)r^2
The above requires r (radius) but the information in the problem provided diameters. But, we know that:
radius = d/2
88,846 miles sphere: radius = 88846/2 = 44423 miles
7,926 miles sphere: radius = 7926/2 = 3963 miles
.
SA of 88,846 miles sphere:
4(3.14159)(44423)^2
= 12.56636(44423)^2
= 12.56636(1973402929)
= 24798491630.86844 square miles
.
SA of 7,926 miles sphere:
4(3.14159)(3963)^2
= 12.56636(3963)^2
= 12.56636(15705369)
= 197359320.78684 square miles
.
Ratio of "SA of 88,846 miles sphere" to "SA of 7,926 miles sphere" then is
24798491630.86844:197359320.78684
= 24798491630.86844/197359320.78684
= 125.651 (this is the ratio)
.
Volume of 88,846 miles sphere:
(4/3)(pi)(44423)^3
= (4.18879)(44423)^3
= (4.18879)(87664478314967)
= 367208090120950.61993 cubic miles
.
Volume of 7,926 miles sphere:
(4/3)(pi)(3963)^3
= (4.18879)(3963)^3
= (4.18879)(62240377347)
= 260711870227.34013 cubic miles
.
Ratio of volumes:
367208090120950.61993:260711870227.34013
367208090120950.61993/260711870227.34013
1408.482
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