Please help me to slove the following question:
[請詳細解釋]
1. The surface areas of two solid spheres made of copper are in the
ratio 4:25. If the larger one weighs 375g, then the smaller one weighs?
Thank you!
S3 Math for area and volume
2011-05-13 4:48 am
回答 (3)
2011-05-13 5:13 am
✔ 最佳答案
weigh ∝ V^3Since the ratio of surface areas is 4 : 25
The ratio of the volumes should be 8 : 125
Let the weigh of the smaller sphere is x g
Then x : 375 = 8 : 125
x = 24 g
2011-05-13 3:54 pm
A1/A2 = 4*pi*r1^2/4*pi*r2^2 = r1^2/r2^2 = 4/25
r1/r2 = 2/5, r1^3/r2^3 = (2^3)/(5^3) = 8/125
V1/V2 = 4/3*pi*r1^3/4/3*pi*r2^3 = r1^3/r2^3 = 8/125
Volume = mass/density, Density d - constant
(m1/d) /(m2/d) = (8/125)
m1/m2 = 8/125
m1 = 375g (8/125) = 24 g
r1/r2 = 2/5, r1^3/r2^3 = (2^3)/(5^3) = 8/125
V1/V2 = 4/3*pi*r1^3/4/3*pi*r2^3 = r1^3/r2^3 = 8/125
Volume = mass/density, Density d - constant
(m1/d) /(m2/d) = (8/125)
m1/m2 = 8/125
m1 = 375g (8/125) = 24 g
2011-05-13 5:17 am
The first line of the answer should be:
weigh ∝ V
weigh ∝ V
收錄日期: 2021-04-15 17:25:22
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110512000051KK00958