標題:
此文章來自奇摩知識+如有不便請留言告知
help.
發問:
A frustum ABCD is cut from a right circular cone VBC of base radius 3cm and height 12cm.The radius of the upper base and the height of the frustum is 2 cm and Hcm respectively.(a)Find H(b)Find the volume of the frustum in terms of πA container in the shape of an inverted hollow iron frustum which is cut from... 顯示更多 A frustum ABCD is cut from a right circular cone VBC of base radius 3cm and height 12cm.The radius of the upper base and the height of the frustum is 2 cm and Hcm respectively. (a)Find H (b)Find the volume of the frustum in terms of π A container in the shape of an inverted hollow iron frustum which is cut from a regular pyramid VABCD.ABCD is a square of side 16cm,and the feight of the container is 6cm (a)the height of the original pyramidVABCD (b)the volume of the container
最佳解答:
Cone problem: (a) Take a view of the diagram below: 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Mensuration1.jpg 【此圖乃本人自製圖片，未經本人同意勿擅自連結或使用】 By the properties of similar triangles, we have: (12-H)/2 = 12/3 12-H = 8 H = 4cm (b) Volume of the frustum = Volume of the original cone - Volume of the cut cone So, the volume is given by: (π/3)(3)2 × 12 - (π/3)(2)2 × (12-4) = 76π/3 cm3 Pyramid problem: (a) Take a view of the diagram below: 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Mensuration2.jpg 【此圖乃本人自製圖片，未經本人同意勿擅自連結或使用】 Since the pyramid is regular, the slant edges (VA, VB, VC and VD) are of the same length as each of the sides of the base. And by Pyth. Thm, we can find out BC = 16√2 cm Then OB (O is mid-point of BC) = 8√2 cm Applying Pyth. Thm again in △VOB, we have VO = 8√2 cm So the height of the original pyramid = 8√2 cm. (b) Now, the cross-sectional view of the pyramid can be shown as follows: 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Mensuration3.jpg 【此圖乃本人自製圖片，未經本人同意勿擅自連結或使用】 The height of the cut pyramid (smaller) has a height of (8√2 - 6) cm. Moreover, since the cut pyramid and the original pyramid are similar solids with their side ratio = (8√2 - 6) : 8√2. So their volume ratio = (8√2 - 6)3 : (8√2)3 according to the property of similar solids. So, we have to find out the volume of the original pyramid first: V = (1/3) × (16)2 × (8√2) = (256/3) × (8√2) cm3 And then the volume of the cut pyramid is given by: V' = (256/3) × (8√2) × [(8√2 - 6)3/(8√2)3] = (256/3) × (8√2 - 6)3 / (8√2)2 = (2/3) × (8√2 - 6)3 cm3 So volume of the container is given by: V - V' = (256/3) × (8√2) - (2/3) × (8√2 - 6)3 cm3 which approximates to a value of 865.4 cm3. (Corr. to 0.1 cm3)
其他解答:
D圖不是你畫|||||A frustum ABCD is cut from a right circular cone VBC of base radius 3cm and height 12cm.The radius of the upper base and the height of the frustum is 2 cm and Hcm respectively. (a)Find H (b)Find the volume of the frustum in terms of π (a) (12-H)/2 = 12/3 H = 4 Height of the frustum is 4 cm. (b) 1/3 π [3^2 x 12 - 2^2 x (12-4)] = 76π/3 Volume of the frustum is 76π/3 cm^2 A container in the shape of an inverted hollow iron frustum which is cut from a regular pyramid VABCD.ABCD is a square of side 16cm,and the feight of the container is 6cm (a)the height of the original pyramidVABCD (b)the volume of the container
留言列表
