Areas and volumes( 幫幫手啊～唔該～～～）

State the base radii and heights of two cylinders A and B which satisfy both the conditions below:
Conditions 1 : volumes of A bigger than volume of B
Assume r = base radii，h = heights
The volumes of cylinders = r2πh
rA2πhA > rB2πhB
rA2hA > rB2hB

Conditions 2 : total surface area of A smaller than total surface of B
A = 2πrh + 2r2π
2πrAhA + 2rA2π < 2πrBhB + 2rB2π
rAhA + rA2 < rBhB + rB2
rA(hA + rA) < rB(hB + rB)

This question is no so difficult. You just need to focus on the formula for calculating volume and surface area.

V = πr²h
A = 2πrh (The curved surface) + 2πr² (The base and the top)
= 2πr(h+r)

We can see that V is more &quot;concentrated&quot; on r than h, the key to make the required cylinders is make one have large radius and small height and the other one have small radius and large height.

Let A to be the one with radius 100 and height 2
Let B to be the one with radius 1.4 and height 9999

Then volume of A
= π(100)²(2) = 20000π

and volume of B
= π(1.4)²(9999) = 19598.04π

Surface area of A
= 2π(100)(2+100) = 20400π

Surface area of B
= 2π(1.4)(9999+1.4) = 28001.12π

There are of course more combinations than this and you may find some more easily.


Hope it helps! ^^

2006-12-13 23:20:00 補充：
Do the questioner know what do the question mean?
This answer is irrelevant with the question.

I am quite disappointed with yajoshua2001