MATHS F.3 10PTS

ddobtn

2010-06-02 6:25 am

圖: http://hk.myblog.yahoo.com/ylf6b05/article?mid=48

the figure shows a right pyramid ,VABCDEF,where O is the centre of the regular hexagonal base.
(a)find the area of ΔOAB.
(b)find the area of ΔVAB.
(c)find the total surface area of the right pyramid VABCDEF.
(d)find the colume of the right pyramid VABCDEF.

回答 (1)

用戶2053

2010-06-02 7:12 am

✔ 最佳答案

圖片參考：http://f20.yahoofs.com/hkblog/bwL__DOT__k4GLHBERJI8S3Dlf_1/blog/ap_20100601102435929.jpg?ib_____DjmjImPGF

a)ΔOAB

= (1/2)*6*6*sin60 = 9√3 cm^2

b) ΔVAB

the height = √(15^2 - (6/2)^2) = 6√6 cm

Area = (1/2) * 6 * 6√6 = 18√6 cm^2

c) Total surface area

= 6 ΔVAB + 6 ΔOAB

= 6 * 18√6 + 6 * 9√3

= 108√6 + 54√3

= 358 cm^2 (3 sig. fig.)

d) The height of the pyramid = √(15^2 - 6^2) = 3√21

Volume = (1/3) Base * h

= (1/3) (6 ΔOAB) (3√21)

= (1/3) (54√3) (3√21)

= 162√7

= 429cm^3 (3 sig .fig.)

👍 0 👎 0