Chapter 11. Q8. Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24cm.
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1 Chapter 11 Q1. The length and breadth of a rectangular field are in the ration 3:2. If the area of the field is 3456 m 2, find the cost of fencing the field at Rs.3.50 per meter. Q2. The cost of turfing a rectangular field at 85 paise per square meter is Rs find the perimeter of the field if its sides are in the ratio 5:3. Q3. The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and perimeter of this garden. 20m 7 m Q4. The dimension of a room are 16X14X10 meters. There are 4 windows of 1.3mx1.4 m and 2 doors of 2mX1m. what will be the cost of white washing the walls and painting the doors and windows, if the rate of white washing is Rs5 per m 2 and rate of painting is Rs8 per m 2. Q5. A room is 7 meter long and 5 meter broad. Is has one door measuring 2m by 1.5m and two windows, each measuring 1.5m by 1m. the cost of painting the walls at Rs12.50 per square meter is RS825. Find the height of the room. Q6. The area of square ABCD is 16cm 2. Find the area of the square joining the mid-points of the sides. Q7. The base of a parallelogram is thrice its height. If the area is 867 cm 2, find the base and height of the parallelogram. Q8. Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24cm. Q9. If the area of rhombus be 24 cm 2 and one of its diagonal AC= 4cm. find the perimeter of rhombus. Q10. An ant is moving around a few food particles of different shapes scattered on the floor. For which food particle would the ant have to take a longer around. Q11. Mrs Kaushik has a square plot as shown in figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house, if cost of developing a garden is Rs.55 per square meter. Page 1
2 Q12. A field in the form of parallelogram has one of its diagonals 42 m long and the perpendicular distance of this diagonal from either of the outlying vertices is 10.8m. find the area of the field. Q13. The diagonal of quadrilateral is 20m in length and the perpendiculars to it from the opposite vertices are 8.5 m and 11m. find the area of the quardrilateral. Q14. In quadrilateral ABCD shown in figure. ABllDC and AD l AB. Also AB = 8m, DC=BC=5m. find the area of the quadrilateral. Q15. Find the area of the shaded region in figure. if ABCD is a square of side 14cm and APD and BPC are semi circle. Q16. A paper is in the form of rectangle ABCD in which AB=20cm and BC=14cm. a semi circular portion with BC as diameter is cut off. Find the area of remaining part. Q17. An athletic track 14m wide consists of two straight section 120m long joining semi-circular ends whose inner radius is 35m. calculate the area of the shaded region. Q18. Find the area of trapezium whose parallel sides are of lengths 10cm and 12cm and the distance between them is 4cm. Page 2
3 Q19. The area of trapezium is 440 cm 2. The length of the parallel sides are respectively 30cm and 14cm. find the distance between them. Q20. The area of trapezium shaped field is 480 m 2, the height is 15m and one of the parallel side is 20m. Find the other side. Q21. Find the altitude of a trapezium, the sum of the length of whose bases is 6.5cm and whose area is 26cm 2 Q22. Find the sum of the lengths of the bases of trapezium whose altitude is 11cm and whose area is 0.55m 2. Q23. The area of the trapezium is 105 cm 2 and its height is 7cm. if one of the parallel sides is longer than the other by 6cm, find the two parallel sides. Q24. The area of a trapezium is 180cm 2 and its height is 12cm. if one of the parallel sides is double that of the other, find the two parallel sides. Q25. The parallel sides of a trapezium are 20cm and 10cm. if non-parallel sides are both equal, each being 13cm. find the area of the trapezium. Q26. If the perimeter of a trapezium be 52cm, its non-parallel sides are equal to 10cm each and its altitude is 8cm, find the area of the trapezium. Q27. The area of a trapezium is 180cm 2 and its height is 9cm. if one of the parallel sides is longer than the other by 6cm, find the two parallel sides. Q28. In the adjoining figure AB ll DC and DA is perpendicular to AB. Further, DC=7cm, CB=10cm and AB=13cm. find the area of the quadrilateral ABCD. Q29. Length of the fence of a trapezium shaped field ABCD is 120m, if BC=48m, CD=17m and AD=40m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC. Q30. The parallel sides DC and AB of a trapezium are 12 cm and 36 cm respectively. Its non-parallel sides area each equal to 15cm. find the area of trapezium. Q1. Find the volume of a cuboid whose a) length =10cm, breadth =8cm, heaight =3cm b) length = 1.5m, breadth =25cm, height =15cm Q2. Find the volume of a cube whose side is 7cm. Part II Q3. A cuboidal wooden block contains 189cm 3 wood. If it be 7cm long and 4.5cm high. Find its breadth. Page 3
4 Q4. Find the height of a cuboid whose volume is 275cm 3 and base area is 25cm 2. Q5. A cubboidal vessel is 10cm long and 8 cm wide. How high must it be made to hold 480 cubic centimeter of liquid. Q6. How many 5 cm cubes can be obtained from a cube whose edge is 20cm. Q7. A match box measures 4cm by 2.5 cm by 1.5cm. what will be the volume of a packet containing 12 such match boxes. How many such packets can be placed in a cardboard box whose size is 60cmx30cmx24cm. Q8. What will happen to the volume of a cube if its edge is doubled. Q9. Three cubes of sides 3cm, 4cm and 5cm are melted and a new cube is formed. Find the side of the new cube. Q10. A rectangular block of ice measures 40cm by 25cm by 15cm. calculate its weight in kg, if ice weight of the weight of the same volume of water and 1 cm 3 of water weight of 1gm. Q11. Eight identical cuboidal wooden blocks are stacked one on top of the other. The total volume of the solid so formed is 128cm 3. If the height of each block is 1 cm and the base is a square, find the dimensions of each block. Q12. Find the volume in cubic meter of each of the cuboid whose dimensions are a) length =10m, breadth=8m and height =2.5m b) length =2m, breadth=1.5m and height =25cm c) length =12m, breadth=35dm and height =50cm Q13. Find the volume in cubic dm of each of the cubes whose side is. a) 1.2m b)25cm c) 1dm5cm Q14. The length breadth and height of a room are 8m, 6.5m and 3.5 m respectively. Find the volume of the air contained in the room. Q15. A room is in the form of cuboid measures 60mx40mx30m. how many cuboidal boxes can be stored in it if the volume of one box is 0.8m 3 Q16. A rectangular water reservoir contains litres of water. Find the depth of the water in the reservoir if its base measures 6m by 3.5 m. Q17. What will be labour charges for digging a cuboidal pit 8m long, 6m broad and 3 m deep at the rate of Rs.20 per m 3. Page 4
5 Q18. How many bricks of size 22cm x 10cm x 7cm are required to construct a wall 33m long, 3.5 high and 40cm thick, if cement and sand used in the construction occupy part of the wall? Q19. A water tank built by a municipality of a town to supply water to its inhabitants at 125 liters per day per person is 40m long and 31.25m broad. The tank, when it is full, can supply water for two days to the inhabitants of the town. Find the depth of the tank. Q20. The earth taken out from a pit is evenly spread over a rectangular field of length 90m, width 60m. if the, volume of the earth dug is 3078m 3. Find the height of the field raised. Q21. A rectangular field is 154m long and 121 m broad. A well of 14m length and 11m breadth is dug inside the field and mud taken out is spread evenly over the remaining part of the filed to a thickness of 25 cm. find the depth of the well. Q22. If the rainfall on a certain day was 5cm. how many litres of water fell on 1 hectare field on that day. Q23. The length, breadth and height of a cuboidal reservoir is 7m, 6m and 15m respectively litre of water is pumped out from the reservoir. find the fall in the water level in the reservoir. Q24. What is the weight of a cubical block of ice 50cm in length, if one cubic meter of ice weight 900 kilogram. Q25. Find the surface area of a chalk box whose length, breadth and height are 16 cm, 8cm and 6cm respectively. Q26. Find the surface area of a cube whose edge is 11cm. Q27. A cuboidal oil tin is 30cm by 40cm by 50cm. find the cost of the tin required for making 20 such tins if the cost of tin sheet is Rs 20 per square meter. Q28. Find the surface area of cube whose volume is 512 m 3. Q29. Find the volume of a cube whose surface area is 54cm 2. Q30. An aquarium is in form of a cuboid whose external measures are 80cm x 30cm x40 cm. the bottom, side faces and back are to be covered with a colour paper. Find the area of the paper needed. Q31. The dimension of a cuboid are in the ratio of 1:2:3 and its total surface area is 88m 2. Find the dimensions. Q32. The paint in a certain container is sufficient to paint an area equal to 9.375m 2. how many bricks measuring 22.5 cm by 10cm by 7.5cm can be painted out of this container. Q33. The measures of text book are 22cm x 11cm x3cm. it is to be covered with a brown paper. If each book requires 164cm 2 of more paper for folding, how much paper is required to wrap 85 such text books. Page 5
6 Q34. Find the area of the four walls of a room whose length is 6m, breadth 5m and height 4m. also, find the cost of white washing the wall, if the rate of white washing is Rs. 5 per square meter. Q35. A swimming pool is 20m in length, 15m in breadth, and 4m in depth. find the cost of cementing its floor and walls at the rate of Rs. 12 per square meter. Q36. The floor of rectangular hall has a perimeter of 250m. its height is 6m. find the cost of painting its four walls at the rate of Rs6 per square meter. Q37. A cuboid has total surface area of 40m 2 and its lateral surface area is 26m 2. Find the area of its base. Q38. Length of a class room is two times its height and its breadth is times its height. The cost of white washing the wall at the rate of Rs 1.60 per m 2 is Rs find the cost of tiling the floor at the rate of Rs per m 2. Q39. The volume of a cuboid is 440 cm 3 and the area of its base is 88cm2. Find its height. Q40. The volume of a cube is 1,000 cm. find its total surface area. Q41. The dimensions of a metallic cuboid are 100cm x 80cm x 64cm. it is melted are recast into a cube. Find the surface area of the cube. Q42. How many 3 meter cubes can be cut from a cuboid measuring 18m x 12m x 9m. Q43. A cube of 9cm edge is immersed completely in a rectangular, vessel containing water. If the dimensions of the base are 15cm and 12 cm, find the rise in water level in the vessel. Q44. The length of a cold storage is double its breadth. Its height is 3 meter. The area of its four walls (including doors) is 108m 2. Find its volume. Q45. Two cubes each of 10cm edge are joined end to end. Find the surface area of the resulting cuboid. Q46. The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm, find the surface area of the cuboid. Q47. A plot of land in the form of a rectangular has a dimension 240m x 180m. a drainlet 10m wide is dug all around it and the earth dug out is evenly spread over the plot. Increasing its surface level by 25cm. find the depth of the drainlet. Q48. Three cubes each of side 5cm are joined end to end. Find the surface are of the resulting cuboid. Q49. Find the number of bricks, each measuring 25cm x 12.5 cm x7.5 cm required to construct a wall 6m long, 5m high and 0.5 m thick, while the cement and sand mixture occupies. Page 6
7 Q50. A metallic sheet is of the rectangular shape with dimensions 48cm x 36cm. from each one of its corners, a square of 8 cm is cut-off. An open box is made of the remaining sheet. Find the volume of the box. Q51.how many planks each of the which is 2m long, 2.5 cm broad and 4 cm thick can be cut-off from a wooden block 6 m long, 15 cm broad and 40 cm thick. Q52. An agriculture field is in the form of a rectangle of length 20m and width 14m. A pit 6m long, 3 m wide and 2.5 m deep is dug in a corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised. Q53. The length of a hall is 20m and width 16m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height and the volume of the hall. Q54. A room is half as long again as it is broad. The cost of carpeting the room at RS.3.25 per m 2 is Rs and the cost of papering the walls at Rs.1.40 per m 2 is Rs if 1 door and 2 windows occupy 8m 2, find the dimensions of the room. Q55. A solid cube is cut into two cuboid of equal volumes. Find the ratio of the total surface area of the given cube and that one one of the cuboids. Q56. The external length, breadth and height of a closed rectangular wooden box are 18cm, 10cm and 6cm respectively and thickness of wood is cm. when the box is empty, its weight 15 kg and when filled with sand it weights 100 kg. find the weight of the cubic cm of wood and cubic cm of sand. Q57. The outer dimensions of a closed wooden box are 10cm by 8 cm by 7cm. thickness of the wood is 1 cm. find the total cost of wood required to make box, if 1 cm 3 of wood costs RS. 2. Part III Q1. Find the curved surface area and total surface area of a right circular cylinder whose height is 15cm and the radius of the base is 7cm. Q2. The diameter of the base of a right circular cylinder is 42cm and its height is 10cm. find the area of the curved surface and total surface area. Q3. Find the height of a cylinder whose radius is 7 cm and total surface area is 968cm 2. Q4.a closed cylindrical tank of radius 1.5m and height 3m is made from a sheet of metal. How much sheet of metal is required. Q5. The curved surface area of a right circular cylinder of height 14cm is 88 cm 2. Find the diameter of the base of the cylinder. Page 7
8 Q6. Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. What should be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25cm with a 3.5cm radius. Q7. The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Find the ratio between the height and radius of the cylinder. Q8. The radii of two right circular cylinder are in the ratio 2:3 and their height are in the ratio 5:4. Calculate the ratio of their curved surface area. Q9. The radius of the base of a cylindrical water drum open at the top is 35cm and height 1.3m. find the inner surface area of the water drum. Q10. In a temple there are 25 cylindrical pillars. The radius of each pillar is 28 cm and height 4m. find the total cost of painting the curved surface area of pillar at the rate of Rs.8 per m 2. Q11. A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 91cm and length is 1.25m. Q12. The diameter of a roller 120 cm long is 84cm. if it takes 500 complete revolutions to level a playground, determine the cost of leveling it at the rate of 30 paise per square meter. Q13. A iron pipe 20cm long has exterior diameter equal to 25cm. if the thickness of the pipe is 1 cm, find the whole surface of the pipe. Q14. A rectangular sheet of paper 44cmx18cm is rolled along its length and a cylinder is formed. Find the radius of the cylinder. Q15. The lateral surface area of hollow cylinder is 4224 cm 2. It is cut along its height and formed a rectangular sheet of width 32cm. find the perimeter of rectangular sheet. Q16. A company packages its milk powder in cylindrical containers whose base has a diameter of 16.8 cm and height 20.5 cm. company places a label around the curved surface of the container. If the label is placed 1.5cm from the top and the bottom. What is the surface area of the label. Q17. Find the volume of a right circular cylinder, if the radius of its base and height are 7cm and 15cm respectively. Q18. The area of the base of a right circular cylinder is 154cm 2 and its height is 15cm. find the volume of the cylinder. Q19. The circumference of the base of a cylinder is 132 cm and its height 25cm. find the volume of the cylinder. Q20. The radii of two right circular cylinder are in the ratio 2:3 and their heights are in the ratio 5:4. Calculate the ratio of curved surface areas and also the ratio of their volumes. Page 8
9 Q21. Two cylinder cans have bases of the same size. The diameter of each is 14cm. one of the cans is 10cm high and the other is 20cm high. Find the ratio of their volumes. Q22. A rectangular sheet of paper 44cm X 18cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder. Q23. A rectangular paper of length 20cm and width 14cm is revolved along its width and a cylinder is formed. Find the volume of the cylinder. Q24. If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original. Q25. The radius and height of a cylinder are in the ratio 5:7 and its volume is 550cm 3. Find its radius. Q26. The volume of a cylinder is 448 π cm 3 and height 7 cm. find its lateral surface area and the total surface area. Q27. The thickness of a hollow cylinder is 2cm. it is 35 cm long and its inner radius is 12 cm. find the volume of the wood required to make the cylinder, assuming it is open at either end. Q28. The thickness of a metallic tube is 1cm and the inner diameter of the tube is 12cm. find the weight of 1m long tube, if the density of the metal be 7.8 gm/cm 3. Q29. A cylindrical road roller made of iron is 1m wide. Its inner diameter is 54cm and thickness of the iron sheet rolled into the road roller is 9cm. find the weight of the roller if 1c.c of iron weight 8gm. (c.c means cubic centimeter) Q30. A well with 10m inside diameter is dug 14m deep. Earth taken out of it is spread all around to a width of 5m to form an embankment. Find the height of embankment. Q31. A circular well of radius 3.5m is dug 20m deep and the earth so dug is spread on a rectangular plot of length 14m and the breadth 11m. find a) volume of the earth dug-out. b) Height of the platform formed by spreading the earth on the rectangular plot. Q32. How many cubic meters of earth must be dug-out to sink a well 22.5 m deep and of diameter 7m. find the cost of plastering the inner curved surface at Rs. 3per square meter. Q33. Find the number of coins, 1.5 cm in diameter and 0.2cm thick, to be melted to form a right circular cylinder of height 10cm and the diameter 4.5cm. Q34. A glass cylinder with diameter 20cm has water to a height of 9cm. a metal cube of 8cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder. Page 9
10 Q35. Into a circular drums of radius 4.2 m and height 3.5m, how many full bags of wheat can be emptied if the space required for wheat in each bag is 2.1 cu.m. Q36. The volume of a metallic cylindrical pipe is 748cm 3. Its length is 14cm and its external radius is 9cm. find its thickness. Q37. The rain water that falls on a roof of area 6160m 2 is collected in a cylindrical tank of diameter 14m and height 10m and thus the tank is completely filled. Find the height of rain water on the roof. Q cubic dm of brass is to be drawn into a cylindrical wire 0.50cm in diameter. Find the length of the wire. Q39. A solid iron rectangular block of dimensions 4.4m, 2.6m and 1m is cast into a hollow cylindrical pipe of internal radius 30cm and thickness 5cm. find the length of the pipe. Q40. A solid cylinder has total surface area of 462 square cm. its curved surface area is one third of its total surface area. Find the volume of the cylinder. Q41. A hollow cylindrical pipe is 21dm long. Its outer and inner diameter are 10 cm and 6cm respectively. Find the volume of the copper used in making the pipe. Q42. The difference between outside and inside surface of a cylindrical metallic pipe 14cm long is 44cm 2. If the pipe is made of 99 cu.centimeters of metal, find the outer and inner radii of the pipe. Q43. An iron pipe 20cm long has exterior diameter equal to 25cm. if the thickness of the pipe is 1 cm, find the whole surface of the pipe. Q44. Find the weight of a lead pipe 3.5m long, if the external diameter of the pipe is 2.4cm and the thickness of the lead is 2mm and 1 cubic cm of lead weights 11gm. Q45. The barrel of a fountain-pen, cylindrical in shape is 7cm long and 5mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre. Q46. The cost of painting the total outside surface of a closed cylindrical oil tank at 60paise per sq. dm is Rs the height of the tank is 6 tank is 6 times the radius of the base of the tank. Find its volume correct to two decimal places. Q47. A lead pencil consists of cylinder of wood with solid cylinder of graphite filled into it. The diameter of the pencil is 7mm, the diameter of the graphite is 1mm and the length of the pencil is 10cm. calculate the weight of the whole pencil, if the specific gravity of the wood is 0.7gm/cm 3 and that of the graphite is 2.1gm/cm 3. Page 10
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