圓錐及扇形英文數學題2(20分)

to do this question, u need to know the following fact first.
it is important because school always exam them

fact:
1) the slant edge of the cone = the radius of the sector
2)the curved surface area of the cone = the area of the sector
3)the base circumference of cone= the arc length of the sector


for the question a
a)
sicne the base circumference of the cone = 10π
2πr = 10π
r = 5
in triangle VOQ
VQ^2=VO^2+OQ^2 (pyth. thm)
h^2=24
h=√24

since the area of the sector = the curved surface area of the cone
therefore,
area of the sector = πrl
=7(√24)π
=107.7341857 cm^2


b)
in triangle VOQ
VQ^2=VO^2+OQ^2 (pyth. thm)
r^2=144
r=12

since the area of the sector = the curved surface area of the cone
therefore,
area of the sector = πrl
= 12(20)π = 240π
= 753.9822369 cm^2


hope the it is helpful for u

ANSWER
請按ANSWER