Consider a circle Let A,C,d,r be the area, circumference, diameter and radius of the circle. Some peoepl establishg the following formulas for the area of a circle.
1. A=1/2Cr 2. A=1/4Cd
3. A=3/4d^2 4. A=1/12c^2
Are the above formulas correct? Give reason
If AUD$1=US$0.7717 and US$1=HK$7.795, then
AUD$1=HK$
HK$1=AUD$
Mathematics (With steps)
2007-08-20 5:53 pm
回答 (2)
2007-08-20 6:26 pm
✔ 最佳答案
1. A=1/2Cr RHS
= 1/2 (2πr)r
=πr²
= A ( LHS)
Therefore formula (1) is correct
2. A=1/4Cd
RHS
= 1/4(2πr)(2r)
=πr²
= A ( LHS)
Therefore formula(2) is correct
3. A=3/4d^2
RHS
= 3/4(2r) ²
= 3r²
does not equal A (LHS)
Therefore formula(3) is incorrect
4. A=1/12c^2
RHS
= 1/12 (2πr)²
= 1/3π²r²
does not equal A (LHS)
Therefore formula(4) is incorrect
Formula (1) and (2) are correct, (3) and (4) are incorrect
AUD$1
= 0.7717 x 7.795
=HK$6.015
HK$1
= 1 ÷ 7.795 ÷0.7717
= AUD$0.1662
2007-08-20 6:26 pm
A=pi*r^2
C=2pi*r
d=2r
1) A=pi*r^2
A=1/2*(2*pi*r)*r
A=1/2*C*r
2) A=1/2*C*r
A=1/4*C*(2*r)
A=1/4*C*d
3) A=pi*r^2
A=1/4*pi*(2*r)^2
A=1/4*pi*d^2 which is bigger than 3/4*d^2
4) A=pi*r^2
A=(1/(4pi))*(2*pi*r)^2
A=(1/(4pi))*C^2 which is smaller than 1/12*C^2
So 1) & 2) is right, and 3) & 4) is wrong
AUD$1=HK$(0.7717*7.795)=HK$6.0154
HK$1=AUD$(1/6.0154)=HK$0.16624
C=2pi*r
d=2r
1) A=pi*r^2
A=1/2*(2*pi*r)*r
A=1/2*C*r
2) A=1/2*C*r
A=1/4*C*(2*r)
A=1/4*C*d
3) A=pi*r^2
A=1/4*pi*(2*r)^2
A=1/4*pi*d^2 which is bigger than 3/4*d^2
4) A=pi*r^2
A=(1/(4pi))*(2*pi*r)^2
A=(1/(4pi))*C^2 which is smaller than 1/12*C^2
So 1) & 2) is right, and 3) & 4) is wrong
AUD$1=HK$(0.7717*7.795)=HK$6.0154
HK$1=AUD$(1/6.0154)=HK$0.16624
收錄日期: 2021-04-13 13:01:34
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070820000051KK00917