數學題 10分

for area of sector (扇形)
you definitely can derive the equation as below by ratio:
consider the ratio of SECTOR / CIRCLE:
angle bound by sector / whole angle of circle (360) =
area of sector / area of circle =
circumference of sector / circumference of circle
a.
120 / 360 = A / [(pi) 9^2]
(1/3) (pi) (81) = A
A = 27(pi)
b.
the circumference of sector becomes the circumference of cup
120 / 360 = C / [2 (pi) 9]
(1/3) (pi) (18) = C
C = 6(pi)
C = 2(pi)r => r = 3
c.
volume of cone/pyramid = 1/3 x base area x height
8.49 = (1/3) (pi 3^2) h
h = 8.49 / (3pi) = ....

a求紙的面積:(以(兀)表示
(圓心角 120度,半徑9cm

1/3 x 兀 x81 =27兀

b求紙杯的半徑
(半徑r,高h,邪高9cm)
1/3 x 2 x 兀x9=18.85 cm
18.85/2兀=3cm
r=3cm

c如果紙杯的高度是8.49cm求紙杯容量(準確至最接近的cm)
1/3 x(兀r^2h) = 1/3x (兀x76.41)=60cm^3