1.Findthe area of each of the following figures.
(a)(b)(c)
(d)(e)(f)
2.Each of the following figures is formed by rectangles. Find the area of the shaded region in each of the following figures.
(a)(b)(c)
(d)(e)(f)
3.Find the area of the shaded region in each of the followingfigures.
(a)(b)(c)
4.Find the area of the shaded region in each of the following figures.
(a)(b)(c)
5.Find the area of the shaded region in each of the following figures.
(a)(b)(c)
6.In the figure, if the area of the shaded region is, find the value of x.
7.In the figure, ABCD is a parallelogram. E is a point on BC such that,and.
(a)Find the area of ABCD.
(b)Find the length of BC.
(c)Find the length of DE.
8.The figure shows quadrilateral PQRS. If M and N are points on QR such that,,and,find the area of quadrilateral PQRS.
[Hint:Let MNxcm.]
9.Find the unknown in each of the following pairs of similar figures.
(a)(b)
10.Find the unknown in each of the following pairs of similar figures.
(a)(b)
11.In the figure, ABCD and AFGE are two similar figures. If the area of AFGE is, find the area of ABCD.
12.In the figure, ABCDEF and APQRST are two similar figures, their respective areas areand. Find the length of PB.
13.In the figure, ABCDEFGH and IJKLMNOP are two similar figures, their total areaisLetbe the area of IJKLMNOP.
(a)Express the area of ABCDEFGH in terms of x.
(b)Find the area of ABCDEFGH and the area of IJKLMNOP.
14.In the figure,. The area of the shaded region and the area of ABC areand respectively.
(a)Find the ratio of the area of ABC to that of ADE.
(b)Find the length of AB.
15.Two pieces of iron wire of different lengths are bent into two similar polygons in the star shape, where the ratio of the lengths of the two pieces of wire is 6:11. If the area of the smaller star is, find the area of the larger star.
16.The scale of the floor plan of a flat is 1cm to 1.5m. If the area of the sitting room on the floor plan is , find its actual area.
[In this exercise, give your answers correct to 1 decimal place if necessary.]
17.Complete the following table. (Take.)
Radius / Diameter / Circumference5cm
12.5cm
20cm
35cm
157cm
266.9cm
18.Find the perimeter of each of the following semi-circles. (Express your answers in terms of .)
(a)(b)(c)
19.The following figures are formed by semi-circles, find the perimeter of each figure. (Express your answers in terms of .)
(a)(b)(c)
20.Find the perimeter of each of the following figures. (Express your answers in terms of .)
(a)(b)(c)
21.Given that the diameters of two circles are 14cm and 16cm respectively, what is the difference in their circumferences? (Express your answer in terms of .)
22.The diameter of a wheel of a bicycle is 0.6m.Find the distance travelled by the bicycle in 20 revolutions of the wheel.
23.The length of the minute-hand of a clock is 12cm.Find the distance moved by the tip of the minute-hand in 45 minutes. (Express your answer in terms of .)
24.Terry jogged around a circular park. Suppose he had completed 4 laps with a total distance of 1250m, find the radius of the park.
25.A rope of 198cm long can wrap around a cylindrical can 6 times. What is the diameter of the base of the can?
26.A coin with the radius of 1.2cm makes 3 revolutions per second on the ground. Find the speed of this coin. (Express your answer in cm/s.)
27.The ratio of the circumferences of two circles is 7:5. What is the ratio of their diameters?
28.The diameter of a car wheel is 48cm. If the wheel makes 550 revolutions per minute, find the speed of the car. (Express your answer in km/h.)
29.The ratio of the circumferences of three circles is 7a:5b:4c. What is the ratio of their radii?
30.The height and the circumference of the base of a right cylindrical container are 20cm and 30cm respectively. Can a square metal plate with the sides of 10cm each be put into the container? Explain briefly.
[In this exercise, give your answers correct to 1 decimal place if necessary.]
31.Complete the following table.
Radius / Diameter / Area5cm
8cm
12cm
30cm
43cm2
95.2cm2
32.The following figures are formed by semi-circles and straight lines, find the area of each figure. (Express your answers in terms of .)
(a)(b)(c)
33.The following figures are formed by semi-circles, find the area of each figure. (Express your answers in terms of .)
(a)(b)(c)
34.The following figure is formed by a quadrant and an isosceles right-angled triangle. Find the area of the shaded region.
35.The diameter of a circular flying disc is 24cm, find its area.
36.The area of a discus is, find its radius.
37.The figure is formed by a quadrant, a semi-circle and a straight line. If the area of the shaded region is , find the value of x.
38.The following figure is formed by quadrants and a square. Find the area of the shaded region.
39.If the radius of a circle decreases by 5%, what is the percentage decrease of the area of the circle?
40.The base areas of two cylindrical cakes are in the ratio of 9:16. Find the ratio of their base diameters.
41.In the figure, the ratio of the radii of two circles is 7:9.
(a)Find the ratio of the area of the smaller circle to that of the larger circle.
(b)If the area of the shaded region is, find the respective areas of the smaller circle and the larger circle.
42.It is given that the length of a necklace is 50cm. What is the area of the circle formed by the necklace?
43.A circular lawn with the area ofis surrounded by fences. Find the length of the fences.
44.In the figure, the door is formed by a semi-circle and a rectangle. If its area is, find its height.
45.In the figure, the width of the wooden frame is 1cm. Find its area.
46.The figure is formed by two squares and a circle.
(a)Find the radius of the circle.
(b)Find the length of the side of the smaller square. (Give your answer correct to 3 significant figures.)
(c)Find the area of the shaded region. (Give your answer correct to 3 significant figures.)
47.Figure I and Figure II are formed by squares and quadrants.
(a)In Figure I,
(i)find the area of region A.
(ii)find the area of region B.
(b)Hence, find the area of the shaded region in Figure II.
(Express your answers in terms of .)
[In this exercise, give your answers correct to 3 significant figures if necessary.]
48.Find the length ofin each of the following figures.
(a)(b)(c)
49.Find the area of sector AOB in each of the following figures.
(a)(b)(c)
50.Find the value of x in each of the following figures.
(a)(b)(c)
51.Find the value of x in each of the following figures.
(a)(b)(c)
52.An arc AB of a circle with the diameter of 25cm subtends an angle of 45 at the centre. Find the length of arc AB.
53.An arc AB of a circle with the diameter of 7cm subtends 66 at the centre at O. Find the area of sector AOB.
54.Find the perimeter of each of the following sectors.
(a)(b)(c)
55.In the figure, O is the centre of arc APC and arc BQD. AEB and CFD are semi-circles. It is given thatand. Find the area of the shaded region.
56.The figure shows a paper fan, whereand. Find the area of ABCD.
57.In the figure, O is the centre, the radius is 8cm,.
(a)Find the area of the shaded region.
(b)Find the perimeter of the shaded region.
58.The figure shows an equilateral triangle ABC with sides of 10cm each. D, E and F are mid-points of the sides of the triangle. A, B and C are the centres of the arcs,andrespectively.
(a)Find the area of the shaded region.
(b)Find the percentage of the shaded area in the figure.
59.An iron wire of length 100cm is bent into a sector OAB as shown in the figure.
(a)If, find the area of sector OAB.
(b)If, find the area of sector OAB.
60.In the figure, OAC and OBD are two similar sectors. The area of the shaded region is. The length of OA is 4 times that of AB.
(a)Find.
(b)Find the area of sector OAC. (Express your answer in terms of .)
61.Thefigure is formed by arc ACB and arc ADB, where O and P are the centres of arc ACB and arc ADB respectively. Is a piece of iron wire with the length of 40cm enough to form the figure? Explain briefly.
62.In the figure, rectangle PQRS is formed by a wire. The wire is now bent into sector OAB.
(a)Find the perimeter of sector OAB.
(b)If the length ofis 10cm, find. (Express your answer in terms of .)
(c)Is the area of sector OAB equal to the area of rectangle PQRS? Explain briefly.
63.In the figure, ABC is an equilateral triangle with sides of 20cm each. The centres of,andare A, Band C respectively. Find the area of the shaded region. (Give your answers correct to 3 significant figures.)
64.In the figure, OAB and PCD are sectors, Chris thought that, do you agree? Explain briefly.
[In this exercise, give your answers correct to 3 significant figures if necessary.]
65.Complete the following table.
Base area of prism / Height of prism / Volume of prism10cm2 / 5cm
25cm2 / 4cm
150cm2 / 600cm3
12cm2 / 180cm3
25cm / 900cm3
60cm / 1080cm3
66.Find the volume of each of the following prisms.
(a)(b)(c)
67.The following are cylinder A and cylinder B. Find the difference in their volumes. (Express your answer in terms of .)
68.A cylindrical cup with the base radius of 5cm is filled with water. If 80 cubes with sides of 1cm each are immersed into the water without overflow,
(a)find the volume of a cube.
(b)find the rise in the water level.
69.The base diameter and the capacity of a cylindrical can are 6.5cm andrespectively. Find the height of the can.
70.A cylindrical metal bar with the radius of 3cm and length of 5cm is melted and recast into a pipe as shown below. Find the length of the pipe.
71.Find the volume of each of the following prisms.
(a)(b)(c)
72.There are 50 rectangular copper bars with dimensions They are melted and recast into a large cuboid with the sides of its square base of 1cm each. Find the height of the large cuboid.
73.The figure shows a copper coin with the diameter of 24mm. In the centre of the coin, there is a square hole with the sides of 5mm each. If the total volume of 50 copper coins is, find the thickness of each copper coin.
74.The figure shows the uniform cross-section of an L-shaped aluminium plate. Each aluminium plate is 120cm long.
(a)Find the volume of a piece of L-shaped aluminium plate in.
(b)It is known that the density of aluminium is. Is it enough to produce 20 pieces of L-shaped aluminium plate with 10kg of aluminium? Explain briefly.
75.The figure shows a spiral staircase with 4 steps. Each step is 15cm high. The uniform cross-section of each step is a sector with the angle at the centre of 30 and radius of 40cm. Find the volume of the spiral staircase.
76.Water flows through a pipe with the inner diameter of 16cm at a speed of 0.8m/s.
(a)Find the volume of water flows out from the pipe per second. (Express your answer in terms of .)
(b)The height and the base radius of a cylindrical tank are 1m and 2m respectively. Can the tank be fully filled by the above pipe in 15 minutes? Explain briefly.
77.If both the base radius and the height of a cylinder increase by 10%, find the percentage increase of its volume.
[In this exercise, give your answers correct to 3 significant figures if necessary.]
78.Find the total surface area of each of the following solids.
(a)(b)(c)
79.Find the total surface area of each of the following prisms.
(a)(b)(c)
80.A metal cuboid with the length of 16cm, width of 8cm and height of 4cm is melted and recast into a cube. Find the total surface area of the cube.
81.The base radius and the height of a cylinder are rcm and hcm respectively. If the sum of the areas of the two bases is equal to the curved surface area of the cylinder, find r:h.
82.The figure shows a cylindrical can with the diameter of 8cm and capacity of. A rectangular packing paper is perfectly fit on the curved surface of the can. Find the area of the packing paper.
83.The length, width and height of a room are 8m, 6m and 2.5m respectively. The total area of a door and a window occupiesof the area of the walls in the room. If the ceiling and the walls are to be painted,
(a)find the total painted area.
(b)Given that the capacity of a tin of paint is 2L and each L of paint can paint an area of, are 10 tins of paint enough to paint the room? Explain briefly.
84.(a)Figure I is formed by two semi-circles with the diameters of 3cm each and a rectangle with dimensions of. Find the area of Figure I.
(b)Figure II shows a candy can with the height of 10cm, and its uniform cross-section is congruent to Figure I. Given that one of its bases and the lateral surface are made of metal which cost 0.8¢/cm2, and the other base is a plastic cover which cost 5¢ each. Find the cost to produce 1000 candy cans. (Give your answer correct to the nearest dollar.)
85.Figure I and Figure II show two containers in the shapes of a cylinder and a square prism respectively. Both the containers are with lids, their heights are both 10cm, and their volumes are both 500cm3. If the material cost of making the containers is 0.1¢/cm2, which container has a lower material cost? Explain briefly.
86.The diameter of a circle is 3.4cm, correct to 2 significant figures.
(a)Find the upper limit and lower limit of the diameter.
(b)Find the possible range of the circumference. (Express your answer in terms of .)
87.The length and width of the cover of a book are 25cm and 18cm respectively, correct to the nearest cm.
(a)(i)Find the upper limit and lower limit of the length of the cover.
(ii)Find the upper limit and lower limit of the width of the cover.
(b)Find the possible range of the area of the cover.
88.The figure shows ABC, where andcorrect to 3 significant figures.
(a)(i)Find the upper limit and lower limit of AD.
(ii)Find the upper limit and lower limit of BC.
(b)Find the possible range of the area of ABC.
89.The figure shows a prism with a trapezium base, whereand , correct to 1 decimal place.
(a)(i)Find the upper limit and lower limit of AB.
(ii)Find the upper limit and lower limit of AD.
(iii)Find the upper limit and lower limit of DC.
(iv)Find the upper limit and lower limit of AF.
(b)Is it possible for the actual volume of the prism to be? Explain briefly.
90.The figure shows a pentagon ABCDE, whereand, correct to the nearest cm.
(a)Find the lower limit of the area of pentagon ABCDE.
(b)If the actual area of pentagon ABCDE is, find the range of values of x.
91.The figure shows the floor plan of a flat.
(a)In the floor plan, measure the lengths of AB, AF, ED and CD. (Give your answers correct to the nearest 0.1cm.)
(b)Given that the scale of the floor plan is 1cm:1.2m, can the area of the flat be? Explain briefly.
10.1