有關similar solid既問題

Cheung Kai Shing, Tomson

2007-01-13 6:51 pm

1.The total surface area of a right circular cone has
increased by 44%.Find the percentage increases in
A)base radius
B)volume
2.If the surface area of aa spherical balloon increases
by 21%,find the percentage increases in
a)radius
b)volume

其實我學左咁耐數學,唔知點解呢個竟然係一個最難的一part,
除左ratio比較之外,個d咩搵出decreasing,increasing in radius等,
要寫勁多條式,雖然都係用返A1/A2=(r1/r2)^2,V1/V2=(r1/r2)^3既
formula,但減黎減去,加黎加去,好煩惱,唔通要死背,有什麼方法
可以掌握呢一課呢?(星期一exam數學)

回答 (1)

myisland8132

2007-01-13 7:00 pm

✔ 最佳答案

1
A)
Assume the original surface area of a right circular cone is A1, the new surface area is A2
then
A2=1.44A1
so
(r2/r1)^2=A2/A1
(r2/r1)^2=1.44
r2/r1=1.2
the percentage increases in base radius is 20%
B)
the ratio of the volume
=(r2/r1)^3
=(1.2)^3
=1.728
the percentage increases in volume is 72.8%
2
A)
Assume the original surface area of a right circular cone is A1, the new surface area is A2
then
A2=1.21A1
so
(r2/r1)^2=A2/A1
(r2/r1)^2=1.21
r2/r1=1.1
the percentage increases in base radius is 10%
B)
the ratio of the volume
=(r2/r1)^3
=(1.1)^3
=1.331
the percentage increases in volume is 33.1%

2007-01-13 11:06:40 補充：
不難﹐你想得太多啦其實不需要做太多加減好似total surface area increase 44%0甘好明顯A2=1.44A1 啦根本上唔需要寫A2=A1(1+44%)=1.44A1 寫得多先費時失事另外﹐那些平方﹐立方都要記一記好似12^2=144, 12^3=1728因為來來去去都是這幾個數﹐記熟了可以加快運算

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