Maths Question

A cone is made from a sector of a circle with radius 8cm which subtends an angle of 216ﾟ. Find:

a. the fraction of the area of the circle used to form the curved surface
the subtends angle of the sector is 216°
therefore, the fraction of the area of the circle used to form the curved surface is 216/360 = 3/5

b. the length of the arc of the circle which forms the circumference of the base
length of the arc = circumference of the circle x the fraction of the sector
　　　　　　　= 2π(8) * 3/5 = 48π/5 cm

c. the radius of the base of the cone
Let r be the radius of the base of the cone
2πr = 48π/5
　r = 24/5 cm

d. the slant height of the cone
the slant height of the cone = the radius of the circle that made the sector
　　　　　　　　　　　　= 8 cm

e. the total surface area of the cone
the surface area of the cone (not include the base circle)
= π (24/5) (8) = 192π/5 cm²　(= 603.186 cm²　--- 3 d.p)

2007-02-26 17:10:15 補充：
你做ge= =

a) 216 / 360 = 3/5
b) 2 X 8 X 3.14 X 3/5 = 30.14 cm (to 2 dec place)
c) 30.144 / 3.14 / 2 = 4.8 cm
d) 8 cm
e) sector area of the circle + cone base area:
(8 X 8 X 3.14 X 3/5) + (4.8 X 4.8 X 3.14) = 192.92 cm2 (to 2 dec place)

Hope this help!