有簡單有困難

1.

Suppose a cylindrical hole is drilled through the centre of a sphere. The length of the hole when measured along its wall is 6 cm. What is the volume of the remaining part of the sphere? (3 marks)

2.

4 people, A, B, C, D need to cross a river at night. There is a bridge that spans the river. However the bridge is only strong enough to hold 2 people at a time. As it is nighttime, a flashlight must be used while crossing the river. A, B, C, D need 10, 5, 2, 1 minute(s) respectively to cross the river, and the battery of the flashlight will run out in 17 minutes. Can everyone cross the river in time ? (2 marks) Please explain. (5 marks)

3. ( 3 marks )

* F_n = the nth Fibonacci Number

Calculate .


4. ( 7 marks )
* Use Heron Formula. (s(s-a)(s-b)(s-c))^0.5 = area of triangle, where a, b, c are the length of the sides of the triangle, and s = (a+b+c)/2



Thanks for answering.

2.
C+D-> -2mins
<-D -1min
A+B-> -10mins
<-C -2mins
C+D-> -2mins

Total:17mins

1. How large is the sphere?

Éireann :1. How large is the sphere?

由於題目已提供 "length of the hole" ，所以沒有提供 "volume of sphere"

MP7697 :

Éireann :1. How large is the sphere?

由於題目已提供 "length of the hole" ，所以沒有提供 "volume of sphere"

Let the radius of the sphere be r
Move the Cartesian coordinate system with the y-axis along the central axis of the hole and the origin at the centre of the sphere
consider the xy plane:

The section of the sphere is x^2+y^2=r^2 -> x^2=r^2-y^2
the section of the cylinder is x^2+3^2=r^2 -> x^2=r^2-3^2
volume = pi in(-3 to 3, y^2-3^2, dy)
又好似真係唔駛...


另外3 好似係1，但係我未有心機爆佢出黎？