F.3 Volume problems

2010-04-01 9:14 pm

In the figure, a solid metal ball rests in a rectangular tray which is PARTLY filled with water. The radius of the metal ball is 2cm. The width and the length of the base of the tray are 7cm and 12cm respectively. The depth of water in the tray is 2cm at present.

a. Find the volume of water ( in cm^3) in the tray.

b. If the height of the tray is 5 cm, find the volume of water (in cm^3) needed to be poured into the tray so that the metal ball is just totally submerged.

answer of a.=151 cm^3
answer of b.=151cm^3

the figure:
http://img188.imageshack.us/img188/4817/mathsg.jpg

i know how to calculate a but not b.
tell me the steps of b.
thanks a lot

回答 (1)

用戶2053

2010-04-01 9:39 pm

✔ 最佳答案

圖片參考：http://img188.imageshack.us/img188/4817/mathsg.jpg

a)7 x 12 x 2 - (1/2)(4/3)(3.1416)(2^3) = 151.24480 cm^3

b)Method 1 :
When the metal ball is just totally submerged , the depth of water in the tray is = the diameter of the ball = 4 cm ,

The volume of the water = 7 x 12 x 4 - (4/3)(3.1416)(2^3) = 302.48960 cm^3

Since there are 151.24480 cm^3 water in the tray ,

302.48960 - 151.24480 = 151.24480 cm^3 = 151cm^3(3sig.) water needed to be poured into the tray so that the metal ball is just totally submerged.

Method 2 :

Since HALF a solid metal ball rests in a rectangular tray which is filled with water. By part a) , we know 151cm^3 water in the tray,
for another HALF , also 151cm^3 water
needed to be poured into the tray so that the metal ball is just totally submerged.

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