# Two F3 Maths Problems

1) Figure 7 shows a piece of Tpblerone chocolate. It has a rectangle base of 30mm(10mm) and slant height of 30mm. The top edge is 4mm in length and located reight aabove the centre of the base. To ease calculation, it is divided vertically into two congruent pyramids and a triangle-based prism as shown in the figure.

(b) Find the angle between planes VAB and ABCD.

(c) Find the volume of the piece of chocolate.

Figure 7:http://postimg.org/image/wo2993543/

2)Figure 8 shows triangle OAB with vertices A(8,0) and B(2,6).OeD and AC are stright lines. OC:CB=1:1 and AD:DB=2:1.

(a) Find the coordinate of C and D.

(b) Find the equation of OD.

(c) Suppose CE:AE=1:k

(1) Find the coordinate of E in terms of k.

(2) By using (b) and (c)(1), find k.

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From Natelie's 意見: the coordinate of C =(1,3) & D=(4,4)

2(b) Find the equation of OD.

(y-0) / (x-0) = (4-0) / (4-0)

y/x= 4/4

y=x

2(c) Suppose CE:AE=1:k

(1) Find the coordinate of E in terms of k.

C=(1,3) & A(8,0)

E=( (1k+8) / (1+k) , (3k+0) / (1+k) )

E is on the line OD, so subsitute the x & y coordinate into the equation of OD

y=x

(1k+8) /(1+k) =3k / (1+k)

1k+8 = 3k

2k=8

k=4 //

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• 2a) The coordinates of C is:

[(2+0)/2 , (6+0)/2]

=(1,3)

The coordinates of D is:

[(8x1)+(2x2)/(2+1) , (0x1)+(6x2)/(2+1)]

=[(8+4)/3 , (0+12)/3]

=(4,4)

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