f.2 maths 20分

(1)

Let A1, A2 be the area of two circles,
and R1, R2 be the radii of two circles.

A1：A2＝4：9
πR1^2：πR2^2＝4：9
R1^2：R2^2＝4：9
∴R1：R2＝2：3

The ratio of the radii of two circles is 2：3.

(2)

Let R be the radius of the circle'
and A be the area of the circle.

A＝πR^2＝π（5^2＋12^2）＝π（25＋144）＝π×169
R^2＝169
R＝13

∴The radius of the circle is 13cm.

(3)

Let P be the perimeter of the circle, R be the radius of the circle,
and A be the area of the circle.

P＝2πR＝30
∴R＝15∕π

A＝πR^2＝π（15∕π）（15∕π）＝225∕π
∴A＝225÷3.14＝71.66（if π＝3.14）

The area of the circle is 71.66 sq cm.【2 decimal places】

(4)

Let R be the radius of the wheel, A be the area of the wheel.

100×2×π×R＝376.8
∴R＝376.8÷200÷π＝1.884∕π

A＝πR^2＝π×（1.884∕π）×（1.884∕π）＝1.1294（if π＝22/7）

The area of the wheel is 1.1294 sqm.【4 decimal places】

1. the ratio of the radii=2:3
2. the radius=square root of(25+144)=13cm
3. 2rx22/7=30
r=30x7/44
area=(210/44)x(210/44)x22/7
=71.6cm2
4. for one revolution, the length=376.8/100=3.768m
2rx22/7=3.768
r=0.6
the area=0.6x0.6x22/7
=1.13m2