F.3 VOLUME問2

2006-12-31 5:51 am

1. Air is leaking out from a sherical balloon.Find the % decrease in its volume when its surface area has decreased by 36%.

2.It is known that nearly 70% of the surface of the Earth are oceans.
The radius of the Earth is 6400km.Find the total area of the oceans on the Earth.

PLZ show the steps.

回答 (1)

myisland8132

2006-12-31 6:20 am

✔ 最佳答案

1
let the radius of the original balloon is r1﹐the radius of the new balloon is r2
surface area has decreased by 36%
4*pi*r2^2=0.64*4*pi*r1^2
r2^2/r1^2=0.64
r2/r1=0.8
the volume of new balloon /the volume of original balloon
=(r2/r1)^3
=0.8^3
=0.512
so the % decrease of volume of new balloon
=1-0.512
=0.488
=48.8%
2
the radius of the Earth is 6400km
the surface area of the Earth
=4*pi*(6400)^2
=514719744 km^2
the total area of the oceans on the Earth.
=0.7*514719744 km^2
=360303820.8 km^2

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