F2 maths

A rope of 376.8 cm long can wrap around a circle 10 times. Find the area of the circle
_____________________
2(pi)r=(376.8)/10
r=6
__________
Area:
(6^2)pi
=113.04
__________________________________
Given that the area of a circle is 2464 cm2 , find its circumference.
(pi)r^2=2464
r=28,-28(rej.)
____________
2pi*28
=176
______________________
Given that the area of a circle is the sum of the areas of two circles with radii 5 cm and 12 cm respectively, find its radius

area of a circle :
5^2(pi)+12^2(pi)
=169pi
______________
r^2(pi)=169pi
r=13,-13(rej.)

1. A rope of 376.8 cm long can wrap around a circle 10 times. Find the area of the circle. (Take π = 3.14.)

Circumference of one circle = 376.8 cm/10 = 37.68 cm
Circumference = π x diameter
37.68 cm = 3.14 x diameter
Diameter = 37.68 cm/3.14 = 12 cm
Radius = diameter/2 = 12 cm/2 = 6 cm
Area of circle = π x radius^2 = 3.14 x (6 cm)^2 = 3.14 x 36 cm^2
Area of circle = 113.04 cm^2

2. Given that the area of a circle is 2464 cm2 , find its circumference. (Take π = 22/7)

Area of circle = π x radius^2
2464 cm2 = 22/7 x radius^2
radius^2 = 2464 cm^2 / (22/7)
radius^2 = 784 cm^2
radius = square root of (784 cm^2) = 28 cm
circumference = 2 x π x radius
circumference = 2 x 22/7 28 cm
circumference = 176 cm

3. Given that the area of a circle is the sum of the areas of two circles with radii 5 cm and 12 cm respectively, find its radius.

radius 1 = 5 cm and radius 2 = 12 cm
Area of circle = area of small circle + area of big circle
Area of circle = π x (radius 1) ^2 + (π x (radius 2)^2
Area of circle = π x (5 cm) ^2 + (π x (12 cm)^2
Area of circle = π x (25 + 144) cm^2
Area of circle = π x 169 cm^2
Area of circle = π x radius^2
π x 169 cm^2 = π x radius^2
radius^2 = 169 cm^2
radius = square root of (169 cm^2)
radius = 13 cm



2011-02-12 12:46:03 補充：
Correction:
In question 2: (missing multiplication sign)
It should be:
circumference = 2 x 22/7 x 28 cm