1. Show that the volume V of a sphere with diameter d and surface area A is given by V= 1/6 Ad.
2. Air is leaking out from a spherical balloon. Find the percentage decrease in its volume when its surface area has decreased by 36%.
中三程度：兩條數學題，求解答
2011-05-22 7:36 pm
回答 (1)
2011-05-22 7:53 pm
✔ 最佳答案
1 V = (4/3)πr^3 where A = 4πr^2So, V = (4πr^2)(1/3)(r) = A(1/3)(d/2) = (1/6)Ad
2 Surface new : Surface original = 0.64 : 1
So, Volume new : Volume original = (√0.64)^3 : 1 = 0.512 : 1
The percentage decrease is (1 - 51.2%) = 48.8%
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