# Practice Test

Q1) The diagonals of two squares are in the ratio of 3 : 2. Find the ratio of their areas. Show Answer

Q2) The base of parallelogram is thrice of its height. If the area of the parallelogram is 2187 sq cm. Find its height. Show Answer

Q3) Find the number of diagonals of a rectangular polygon having 12 sides. Show Answer

Q4) The side of a square is 5 cm which is 13 cm less than the diameter of a circle. What is the approximate area of the circle? Show Answer

Q5) If the length of a rectangle increases by 3% and the breadth decreases by 4%, then find the percentage change in area. Show Answer

Q6) If area of a square is 64 sq cm, then find the area of the circle formed by the same perimeter. Show Answer

Q7) Find the area of a square inscribed in a circle of radius 4 cm. Show Answer

Q8) The largest triangle is inscribed in a semicircle of radius 4 cm. Find the area inside the semicircle, which is not occupied by the triangle. Show Answer

Q9) The area of a rectangle is 4 times the area of a square. The area of the square is 729 sq cm and the length of the rectangle is 81 cm. What is the difference between the side of the square and the breadth of the rectangle? Show Answer

Q10) The length of a rectangle is twice its breadth. If the length is decreased by half of the 10 cm and the breadth is increased by half of the 10 cm, the area of the rectangle is increased by 5 sq cm more than 70 sq cm. Find the length of the rectangle. Show Answer

Q11) A 7 m wide road runs outside around a circular park whose circumference is 176 m. Find the area of the road. Show Answer

Q12) The perimeters of two squares are 68 cm and 60 cm. Find the perimeter of the third square whose area is equal to the difference of the areas of these two squares. Show Answer

Q13) One diagonal of a rhombus is 60% of the other diagonal. Then, area of the rhombus is how many times the square of the length of the larger diagonal? Show Answer

Q14) The hand of a clock are 10 cm and 7 cm, respectively. Find the difference between the distance traveled by their extremities in 3 days 5 h. Show Answer

Q15) The radius of a circle is 75 cm. A zone of that circle has one of its parallel chords coinciding with the diameter and the other equal to the radius. Find the area of that zone. Show Answer

Q16) A took 15 s to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to across the same field along its sides walking at the rate of 68 m/per min. Find the area of the field. Show Answer

Q17) Two sides of a triangle are 85 m and 154 m and the perimeter is 324 m. Find the area of the triangle. Show Answer

Q18) The sides of a triangle are 25 m, 39 m and 56 m, respectively. Find the perpendicular from the opposite angle on the greatest sides. Show Answer

Q19) If sides of a square are increased by 5%, by what per cent, its area will be increased? Show Answer

Q20) The diameter of the base of a right circular cone is 14 m while its slant height is 9 m. Find the volume of the cone. Show Answer

Q21) Find the length of the longest pole that can be kept in a room 5 m long, 4 m broad and 3 m high. Show Answer

Q22) If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be Show Answer

Q23) If the radius of a sphere is increased by 3%, what per cent increase takes place in surface area of the sphere? Show Answer

Q24) If the radius of a cylinder is increased by 25% and its height remains unchanged, then find the per cent increase in volume. Show Answer

Q25) Seven equal cubes each of side 5 cm are joined end-to-end. Find the surface area of the resulting cuboid. Show Answer

Q26) A cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm. If the top most ball touches the upper cover of the box, then volume of the empty space in the box is Show Answer

Q27) Three cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find half the square area of the new cube Show Answer

Q28) How many bullets can be made out of a lead cylinder 56 cm high having a radius of 6 cm, each bullet being 1.5 cm in diameter. Show Answer

Q29) A cone has height half of 16.8 cm while diameter of its base is 4.2 cm. It is melted and recast into a sphere. Find the surface area of the sphere. Show Answer

Q30) A tank is 7 m long and 4 m wide. At what speed should water run through a pipe 5 cm broad and 4 cm deep, so that in 6 h and 18 min water level in the tank rises by 4.5 m? Show Answer

Q31) The length, breadth and height of a room are 5 m, 4 m and 3 m, respectively. Find the cost of white washing the walls of the room and selling at the rate of Rs. 7.50 per sq m. Show Answer

Q32) The diameter of a roller is 84 cm and its length 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in sq m. Show Answer

Q33) A hemispherical bowl has 3.5 cm radius. It is to be painted inside as well as outside. Find the cost of painting it at the rate of Rs. 5 per 10 sq cm. Show Answer

Q34) A solid cube of side 12 cm is cut into eight cubes of equal volumes. Find the ratio between the surface areas of bigger and small cubes. Show Answer

Q35) How many coins 1.4 cm in diameter and 0.4 cm thick is to be melted to form a right circular cylinder of height 16 cm and diameter 3.5 cm. Show Answer

Q36) Find the volume of the largest right cone that can be cut out of a cube whose edge is 4.4 m Show Answer

Q37) A right cone and a hemisphere lie on opposite sides of a common base of 2.5 m diameter and the cone is right angled at the vertex. If a cylinder circumscribe them in this position, what additional space will be enclosed? Show Answer

Q38) The base of a prism is a triangle of sides 3 m, 4 m and 5 m respectively. The height of the prism is 10 m. What is the volume of prism? Show Answer

Q39) The base of a right prism is an equilateral triangle with a side of 7 m and its height is 24 m. What is the volume of prism? Show Answer

Q40) The base of a right prism is a square with a side of 2 cm and its height is 10 cm, then what is the total surface area of prism? Show Answer

Q41) A right pyramid 15 cm high has a square base for which the side is 16 cm. What is the curved square area of the pyramid? Show Answer

Q42) The length, breadth and height of a room are in the ratio 3 : 2 : 1. The length, breadth and height of the room are increased by 300%, 200% and 100%, respectively. Find how many number of times the volume of the room is increased? Show Answer

Q43) A right circular cone has height of 12 cm and base diameter of 70 cm. Find the cone of the volume Show Answer

Q44) A hemispherical bowl is made of steel and 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved area of the bowl? Show Answer

Q45) A frustum of right circular cone has a diameter of base and top 20 cm and 12 cm, respectively and height of 10 cm. Find the area of its whole surface and volume. Show Answer

Q46) If side of a cube is increased by 10%, by how much per cent does its volume increase? Show Answer

Q47) A right pyramid 10 m high has a square base for which the diagonal is 10 m. What is the volume and lateral surface area of this pyramid? Show Answer

Q48) The integral base of an isosceles triangle can be, whose area is 60 cm and the length of one of the equal sides in 13 cm. Show Answer

Q49) Area of circle is equal to the area of a rectangle having perimeter of 50 cm and the length is more than its breadth by 3 cm. What is the diameter of the circle? Show Answer

Q50) A ladder is resting with one end in contact with the top of a wall of height 60 m and the other end on the ground is at a distance of 11 m from the wall. The length of the ladder is Show Answer

Q51) The circumference of a circle is equal to the perimeter of a rectangle. The length and the breadth of the rectangle are 45 cm and 43 cm, respectively. What is the half the radius of the circle? Show Answer

Q52) A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6 : 5. Find the 25% of the smaller side of the rectangle. Show Answer

Q53) The base of a triangular field is three times its height. If the cost of cultivating the field is Rs. 36.72 per hectare is Rs. 495.72. Find the height and base of the triangular filed. Show Answer

Q54) In a swimming pool measuring 90 m by 40 m, 150 men take a dip. If the average displacement of water by a man is 8 m. What will be the rise in water level? Show Answer

Q55) A hemispherical basin of 150 cm diameter hold water one hundred and 20 times as much as a cylindrical tube. If the height of the tube is 15 cm, then the diameter of the tube is Show Answer

Q56) How many metres of cloth 10 m wide will be required to make a conical tent with base radius of 14 m and height is 48 m? Show Answer

Q57) A copper sphere of diameter 36 cm is drawn into a wire of diameter 4 mm. Find the length of the wire. Show Answer

Q58) A well with 28 m inside diameter is dug 8 m deep. The earth taken out of it has been evenly spread around it to a depth of 21 m to form an embankment. Find the height of the embankment. Show Answer

Q59) A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle? Show Answer

Q60) If the perimeter and diagonal of a rectangle are 14 and 5 cms respectively, find its area. Show Answer

Q61) In an isosceles right angled triangle, the perimeter is 20 meter. Find its area. Show Answer

Q62) In a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 meters respectively. Find its area. Show Answer

Q63) A horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long. Over how much area of the field can it graze? Show Answer

Q64) From a square piece of a paper having each side equal to 10 cm, the largest possible circle is being cut out. The ratio of the area of the circle to the area of the original square is nearly Show Answer

Q65) If the area of a circle decreases by 36%, then the radius of a circle decreases by Show Answer

Q66) The floor of a rectangular room is 15 m long and 12 m wide. The room is surrounded by a verandah of width 2 m on all its sides. The area of the verandah is Show Answer

Q67) A cylindrical bucket of height 36 cm and radius 21 cm is filled with sand. The bucket is emptied on the ground and a conical heap of sand is formed, the height of the heap being 12 cm. The radius of the heap at the base is Show Answer

Q68) The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. The area of the triangle is Show Answer

Q69) The cross section of a canal is a trapezium in shape. If the canal is 7 meters wide at the top and 9 meters at the bottom and the area of cross-section is 1280 square meters, find the length of the canal. Show Answer

Q70) It is required to fix a pipe such that water flowing through it at a speed of 7 meters per minute fills a tank of capacity 440 cubic meters in 10 minutes. The inner radius of the pipe should be Show Answer

Q71) A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet? Show Answer

Q72) A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper? Show Answer

Q73) The length and breadth of the floor of the room are 20 feet and 10 feet respectively. Square tiles of 2 feet length of different colours are to be laid on the floor. Black tiles are laid in the first row on all sides. If white tiles are laid in the one-third of the remaining and blue tiles in the rest, how many blue tiles will be there? Show Answer

Q74) Four equal circles are described about the four corners of a square so that each touches two of the others. If a side of the square is 14 cm, then the area enclosed between the circumferences of the circles is Show Answer

Q75) The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the part (in sq. m.) is Show Answer

Q76) The water in a rectangular reservoir having a base 80 meters by 60 meter is 6.5 meters deep. In what time can the water be emptied by a pipe whose cross section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km per hour? Show Answer

Q77) The ratio of height of a room to its semi-perimeter is 2 : 5. It costs Rs. 260 to paper the walls of the room with paper 50 cm wide at Rs. 2 per meter allowing an area of 15 sq. m for doors and windows. The height of the room is Show Answer

Q78) Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart, towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is Show Answer

Q79) A metal cube of edge 12 cm is melted and formed into the smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, then find the edge of the third smaller cube. Show Answer

Q80) The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 300%, respectively. Then, the increase in the volume of the cuboid will be Show Answer

Q81) A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter of 0.2 cm. The length of the wire is Show Answer

Q82) How many spherical bullets can be made out of a lead cylinder 28 cm high and with base radius 6 cm, each bullet being 1.5 cm in diameter? Show Answer

Q83) A spherical ball of lead, 3 cm in diameter, is melted and recast into three spherical balls. The diameter of two of these balls are 1.5 cm and 2 cm respectively. The diameter of the third ball is Show Answer

Q84) A conical vessel, whose internal radius is 12 cm and height 50 cm, is full of liquid. The contents are emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the liquid rises in the cylindrical vessel. Show Answer

Q85) The trunk of a tree is a right cylinder 1.5 m in radius and 10 m high. The volume of the timber which remains when the trunk is trimmed just enough to reduce it to a rectangular parallelepiped on a square base is Show Answer

Q86) The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of cube having 8 feet each side? Show Answer

Q87) A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is Show Answer

Q88) A reservoir is supplied from a pipe 6 cm in diameter. How many pipes of 3 cms diameter would discharge the same quantity, supposing the velocity of water is same? Show Answer

Q89) A conical cavity is drilled in a circular cylinder of 15 cm height and 16 cm base diameter. The height and the base diameter of the cone are same as those of the cylinder. Determine the total surface area of the remaining solid. Show Answer

Q90) An ice-cream company makes popular brand of ice-cream in rectangular shaped bar 6 cm long, 5 cm wide and 2 cm thick. To cut the cost, the company has decided to reduce the volume of the bar by 20%, the thickness remaining the same, but the length and width will be decreased by the same percentage amount. The new length L will satisfy Show Answer

Q91) Water flows through a cylindrical pipe of internal diameter 7 cm at 2 m per second. If the pipe is always half full, then what is the volume of water (in liters) discharged in 10 minutes? Show Answer

Q92) A semicircular sheet of paper of diameter 28 cm is bent to cover the exterior surface of an open conical ice-cream cup. The depth of the ice-cream cup is Show Answer

Q93) A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is Show Answer

Q94) A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is Show Answer

Q95) A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is Show Answer

Q96) A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, then find the radius of the ice-cream cone. Show Answer

Q97) A cylinder is filled to 4/5 th its volume. It is then filled so that the level of water coincides with one edge of its bottom and top edge of the opposite side. In the process, 30 cc of the water is spilled. What is the volume of the cylinder? Show Answer

Q98) There are two concentric circular tracks of radii 100 m and 102 m, respectively. A runs on the inner track and goes once round on the inner track in 1 min 30 sec, while B runs on the outer track in 1 min 32 sec. Who runs faster? Show Answer

Q99) A monument has 50 cylindrical pillars each of diameter 50 cm and height 4 m. What will be the labour charges for getting these pillars cleaned at the rate of 50 paise per sq. m.? Show Answer

Q100) A conical vessel of base radius 2 cm and height 3 cm is filled with kerosene. This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius 2 cm. The kerosene level in the jar is Show Answer

Q101) In a swimming pool measuring 90 m by 40 m, 150 men take a dip. If the average displacement of water by a man is 8 cubic meters, what will be the rise in water level? Show Answer

Q102) A square is inscribed in a circle of radius 8 cm. The area of the square is Show Answer

Q103) The biggest possible circle is inscribed in a rectangle of length 16 cm and breadth 6 cm. Then its area is Show Answer

Q104) If the diagonal of a square is doubled, then its area will be Show Answer

Q105) A metal pipe of negligible thickness has radius 21 cm and length 90 cm. The outer curved surface area of the pipe in square cm is Show Answer

Q106) The base of a right pyramid is an equilateral triangle of side 4 cm each. Each slant edge is 5 cm long. The volume of the pyramid is Show Answer

Q107) There are two conses. The curved surface are of a one is twice that of the other. The slant height of the latter is twice Show Answer

Q108) The radius of a right circular cone is 3 cm and its height is 4 cm. The total surface area of the cone is Show Answer

Q109) A sphere is placed inside a right circular cylinder so as to touch the top, base and the lateral surface of the cylinder. If the radius of the sphere is R, the volume of the cylinder is Show Answer