volume and similar figure

[匿名]

2010-03-13 9:26 pm

1. A cylinder of radius 9cm is filled with some water. Six identical metal spheres of radiu 2cm are sunk completely into the water . By how much does the level
increase?

2.If the surface area of a spherical balloon is increased by 44%, find the percentage changed in its volume?

回答 (1)

用戶2053

2010-03-13 10:05 pm

✔ 最佳答案

1)Let x cm be the level increase :
The water increase part volume of the cylinder = x * TT (9)^2
So x * TT (9)^2 = The volume of Six identical metal spheres
x * TT (9)^2 = 6 * (4/3)TT (2)^3
81x = 64
x = 64/81
The level increase 64/81 cm
2)
Let r be the original radius and R be the increased radius :
r^2 : R^2 = 1 : (1+44%) = 1 : 1.44 = 25 : 36
r : R = 5 : 6 , so :
The old volume : the new volume
= r^3 : R^3
= 5^3 : 6^3
= 125 : 216
the percentage changed in its volume
= [(216 - 125) / 125] * 100%
= + 72.8%
Increased by 72.8%

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