F.3 Maths5點 (2 Questions only)

[匿名]

2011-10-17 6:35 am

1. Mrs.Lee invests 3/8 of his annual salary at a simple interest rate of 12%p.a.. If the return of his investment is 10800 in a year, what is his monthy salary?

ANS let$y be the annual salary.
3/8y*12%*1=10800
y=240000
monthy salary=240000/12=20000

***** I don't know why the question said the return is 10800, that means the amount, right? but it calculate as interest.....

2. if a large cube is cut into 8 smaller cubes, then the percentage increase of the surface area is?

ANS Let a be the side length of one of the smaller cubes is 1/2a.

surface area of the large cube =6a^2
surface area of the smaller cube
=(1/2a)^2 *6 =3/2a^2
Surface area of 8 smaller cubes=3/2a^2 *8=12a^2

Percentage increase = 12a^2-6a^2/6a^2 *100% = 100%

I really don't understand what is going on with this whole ans.... Please explain to me step by step.....i need your patience.

THANK YOU SO MUCH~~~~~~~~

回答 (1)

Herman Tam

2011-10-17 8:11 am

✔ 最佳答案

Question 1
Return means 回報, i.e. for deposit, the return should be the total interest incurred. I think the step for the answer is already very clear.

Question 2
When a large cube is cut into 8 identical smaller sqrare cubes, the side of each side should be a/2
You can imagine how a cube a x a is cut into 8 identical cubes. Each side of each cube should a/2.
since one cube should have six faces,
surface area of one cube should be (a/2)^2 * 6 = 3/2 a^2
total surface area of 8 small cube should be equal to 8 x 3/2 a^2 = 12a^2
Percentage increase = (new - old)/ old
originally, the surface area of the large cube = 6 x a^2 =6a^2

Percentage increase = (12a^2- 6a^2)/6a^2
=1 = 100%

參考: ME

👍 0 👎 0