Stage 3:
1. The diagram below shows some of the solid cylinders.
The radius and height of each following cylinder are reduced by 1 cm respectively.
The solid cylinder is put in the order of size into a water tank, resulting the water n
the tank to overflow continuously into a measuring cylinder. The volume of water in
the measuring cylinder is measured after each addition. The table below shows the
volume of water measured.
Given the height of the second cylinder is 29cm .
(a) Find the volume of the tenth cylinder.
(b) Find the cylinder which has total surface area of 144π 𝑐𝑚2 .
2.
The following diagram shows a form of a pattern on the floor. Given that the size
of the room is 6 m x 6 m and the size of a piece of the tile is 30 cm x 30 cm.
(a) How many red tiles are needed?
(b) Find the difference between the number of red tiles and yellow tiles.
2. A wire of length 500π cm is cut into 20 semicircular arcs as shown in diagram 2. The
radius of each semicircular arc is longer than the preceding by 2 cm.
Calculate:
(a) The length, in terms of π, of the smallest circular arc.
(b) The number of semicircular arcs that can be obtained if a wire of length 1050π
cm is used.