Multiple choice questions (MCQ) on Area and volume
1. A man walking at the rate 3 km/hr crosses a square field diagonally in 1 minute. What is the area of the field?
a. 1000 m2 b. 1250 m2 c. 2500 m2 d. 5000 m2
2. From a rectangular metal sheet of sides 25 cm and 20 cm, a circular sheet as large as possible is cut-off. What is the area of the remaining sheet?
a. 186 cm2 b. 144 cm2 c. 93 cm2 d. 72 cm2
3. The difference between the area of a square and that of an equilateral triangle on the same base is ¼ cm2. What is the length of side of triangle?
a. (4 – √3)1/2 b. (4 + √3)1/2 c. (4 – √3)1/2 d. (4 + √3)1/2
4. Three cubes each of side 5 cm are joined end to end. What is the surface area of the resulting cuboid?
a. 300 cm2 b. 350 cm2 c. 375 cm2 d. 400 cm2
5. A horse is tied to a pole fixed at one corner of a 50 m x 50 m square field of grass by means of a 20 m long rope. What is the area of that part of the field which the horse can graze?
a. 1256 m2 b. 942 m2 c. 628 m2 d. 314 m2
6. The diameter of the moon is approximately one-fourth of that of the earth. What is the (approximately) ratio of the volume of the moon to that of earth?
a. 1/16 b. 1/32 c. 1/48 d. 1/64
7. What is the area of a right angled isosceles triangle whose hypotenuse is 6√2 cm?
a. 12 cm2 b. 18 cm2 c. 24 cm2 d. 36 cm2
8. A lead pencil is in the shape of a cylinder. The pencil is 21 cm long with radius 0.4 cm and its lead is of radius 0.1 cm. What is the volume of wood in the pencil?
a. 9.0 cm3 b. 9.4 cm3 c. 9.9 cm3 d. 10.1 cm3
9. If A is the area of a triangle in cm2, whose sides are 9 cm, 10 cm and 11 cm, then which one of the following is correct?
a. A ˂ 40 cm2 b. 40 cm2 ˂ A ˂ 45 cm2
c. 45 cm2 ˂ A ˂ 50 cm2 d. A ˃ 50 cm2
10. A roller of diameter 70 cm and length 2 m is rolling on the ground. What is the area covered by the roller in 50 revolutions?
a. 180 m2 b. 200 m2 c. 220 m2 d. 240 m2
11. A cylindrical rod of length h is melted and cast into a cone of base radius twice that of the cylinder. What is the height of the cone?
a. 3h/4 b. 4h/3 c. 2h d. h/2
12. A cylindrical vessel of base radius 14 cm is filled with water to some height. If a rectangular solid of dimensions 22 cm x 7 cm x 5 cm is immersed in it, what is the rise in water level?
a. 0.5 cm b. 1.0 cm c. 1.25 cm d. 1.5 cm
13. Three circular laminas of the same radius are cut from a larger circular lamina. When the radius of each lamina cut out is the largest possible, then what is the ratio (approximate) of the area of the residual piece of the original lamina to its original total area?
a. 0.30 b. 0.35 c. 0.40 d. 0.45
14. The volume of a cone is equal to that of sphere. If the diameter of base of cone is equal to the diameter of the sphere, what is the ratio of height of cone to the diameter of the sphere?
a. 2:1 b.1:2 c.3:1 d.4:1
15. The length, breadth and height of a rectangular parallelepiped are in ratio 6:3:1. If the surface area of a cube is equal to the surface area of this parallelepiped; then what is the ratio of the volume of the cube to the volume of the parallelepiped?
a. 1:1 b. 5:4 c. 7:5 d. 3:2
16. A rectangular tank whose length and breadth are 2.5 m and 1.5 m respectively is half full of water. If 750 litre more water is poured into the tank, what is the height through which water level further goes up?
a. 18 cm b. 20 cm c. 15 cm d. 200 cm
17. Two similar parallelograms have corresponding sides in the ratio 1:k. What is the ratio of their areas?
a. 1:3k2 b. 1:4k2 c. 1:k2 d. 1:2k2
18. A cylinder having base of circumference 60 cm is rolling without sliding at a rate of 5 rounds per second. How much distance will the cylinder roll in 5 seconds?
a. 15 m b. 1.5 m c. 30 m d. 3 m
19. A semi circular thin sheet of a metal of diameter 28 cm is bent and an open conical cup is made. What is the capacity of the cup?
a. (1000/3)√3 cm3 b. 300√3 cm3 c. (700/3)√3 cm3 d. (1078/3)√3 cm3
20. A hemispherical bowl of internal radius 20 cm contains sauce. The sauce is to be filled in conical shaped bottles of radius 5 cm and height 8 cm. What is the number of bottles required?
a. 100 b. 90 c. 80 d. 75
21. A hemisphere is made of a sheet of a metal 1 cm thick. If the outer radius is 5 cm, what is the weight of the hemisphere (1 cm3 of the metal weighs 9 g)
a. 54 П g b. 366 П g c. 122 П g d. 108 П g
22. A sphere and a cube have same surface area. What is the ratio of the square of volume of the sphere to the square of volume of the cube?
a. П:6 b. 1:1 c. 6:П d. 3:П
23. The inner and outer radii of a 7 m long hollow iron right circular cylindrical pipe are 2 cm and 4 cm respectively. If 1000 cm3 of iron weighs 5 kg, what is the weight of the pipe?
a. 264 kg b. 132 kg c. 396 kg d. None of the above
24. What is the maximum area of a rectangle, the perimeter of which is 18 cm?
a. 20.25 cm2 b. 20.00 cm2 c. 19.75 cm2 d. 19.60 cm2
25. The diameter of a circle circumscribing a square is 15√2 cm. What is the length of the side of the square?
a. 15 cm b. 12 cm c. 10 cm d. 7.5 cm
26. What is the length of the perpendicular drawn from the centre of circle of radius r on the chord of length √3 r?
a. r b. √2 r c. r/2 d. r/4
27. The area of a rectangle whose length is 5 units more than twice its width is 75 square units. What is its width?
a. 3 units b. 5 units c. 7 units d. 10 units
28. If the diameter of a sphere is doubled, how does its surface area change?
a. It increases two times b. It increases three times
c. It increases four times d. It increases eight times
29. What is the number of wax balls, each of radius 1 cm, which can be molded out of a sphere of radius 8 cm?
a. 256 b. 512 c. 768 d. 1024
30. Cylindrical pillars of a building have to be painted. The diameter of each pillar is 70 cm and the height is 4m. What is the cost of painting at the rate of Rs. 5 per square metre?
a. Rs. 400 b. Rs. 440 c. Rs. 480 d. Rs. 500
31. A sphere is inscribed in a cubical box such that the sphere is tangent to all six faces of the box. What is the ratio of the volume of the cubical box to the volume of sphere?
a. 6П b. 36П c. 4П/3 d. 6/П
32. The areas of two circles are in the ratio of 1:2. If the two circles are bent in the form of squares, what is the ratio of their areas?
a. 1:2 b. 1:3 c. 1:√2 d. 1:4
33. The radii of two cylinders are in the ratio 2:3 and their curved surface areas are in the ratio 5:3. What is the ratio of their volumes?
a. 20:27 b. 10:9 c. 9:10 d. 27:20
34. A grassy field has the shape of an equilateral triangle of side 6 m. A horse is tied to one of its vertices with a rope of length 4.2 m. The percentage of the total area of the field which is available for grazing is best approximated by
a. 50% b. 55% c. 59% d. 62%
35. The radii of the circular ends of a bucket of height 40 cm are of lengths 35 cm and 14 cm. What is the volume of the bucket?
a. 60060 cubic cm b. 70040 cubic cm c. 80080 cubic cm d. 80160 cubic cm
36. From a solid cylinder of height 4 cm and radius 3 cm, a conical cavity of height 4 cm and of base radius 3 cm is hollowed out. What is the total surface area of the remaining solid?
a. 15П sq cm b. 22П sq cm c. 33П sq cm d. 48П sq cm
37. A circle circumscribes a rectangle with sides 16 cm and 12 cm. What is the area of the circle?
a. 48П square cm b. 50П square cm c. 100П square cm d. 200П square cm
38. What is the area of an equilateral triangle having altitude equal to 2√3 cm?
a. √3 square cm b. 2√3 square cm c. 3√3 square cm d. 4√3 square cm
39. The surface area of a sphere is 616 square cm. If its radius is changed so that the area gets reduced by 75% then the radius becomes
a. 1.6 cm b. 2.3 cm c. 2.5 cm d. 3.5 cm
40. A cylindrical vessel of height 10 cm has base radius 60 cm. If d is the diameter of a spherical vessel of equal volume, then what is d equal to?
a. 30 cm b. 60 cm c. 90 cm d. 120 cm
41. A cylindrical tank 7 m in diameter contains water to a depth of 4 m. What is the total area of wetted surface?
a. 110 m2 b. 126.5 m2 c. 131.5 m2 d. 136.5 m2
42. A wall is of the form of a trapezium with height 4 m and parallel sides being 3 m and 5 m. What is the cost of painting the wall, if the rate of painting is Rs. 25/- per square metre?
a. Rs 240 b. Rs. 400 c. Rs. 480 d. Rs. 800
43. A lawn 30 m long and 16 m wide is surrounded by a path 2 m wide. What is the area of the path?
a. 200 m2 b. 280 m2 c. 300 m2 d. 320 m2
44. A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. What is the height of the cone?
a. 12 cm b. 14 cm c. 17 cm d. 18 cm
45. The width of a rectangle is 4x which is only 25% of its length. What are the area and the perimeter of the rectangle respectively?
a. 16x2 sq unit and 16x unit b. 20x2 sq unit and 40x unit
c. 32x2 sq unit and 64x unit d. 64x2 sq unit and 40x unit
46. A square field whose area is 36m2 and a rectangular lawn whose width is 2/3 of the side of square field have the same perimeter. The area (in m2) of the lawn is
a. 32 b. 48 c. 64 d. 24
47. A box with inside measurements 60 cm x 30 cm x 24 cm is full of wooden cubes of the same size. If the number of cubes is 25, then the side (in cm) of each cube is
a. 9 b. 12 c. 18 d. 6
48. Circumference of the base of a right circular cylinder is 44 cm and its height is 15 cm. The volume (in cm3) of the cylinder is (Take П = 22/7)
a. 1155 b. 1540 c. 2310 d. 770
49. A polygon has a perimeter of 16 cm and an area of 16 cm2. The shape of the polygon is a
a. square b. hexagon c. rectangle which is not a square d. triangle