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Q1. A water tank is in a form of cube with edge 2 m. Find its volume.

• 8 m³
• 16 m³
• 4 m³
• 12 m³

Solution

Volume of cube = a³ Edge of cubical tank = 2 m Volume of cubical tank = 2 x 2 x 2 = 8 m³.

Q2. A cuboidal box with sides 21 cm x 20 cm x 18 cm is to be filled with cuboidal boxes with sides 7 cm x 6 cm x 5 cm. How many cuboids can be placed in it? 

• 20
• 22
• 26
• None

Solution

number of cuboids = =  = 36 

Q3. If the perimeter of a square is 36 m then its area is:

• 84 m²
• 80 m²
• 72 m²
• 81 m²

Solution

Perimeter of square = 36 m Side of square =  = 9 m Thus, Area of square = 9 x 9 = 81 m²

Q4. Total surface area of a cube is 600 sq. cm. So the perimeter of each of its faces is ______.

• 30 cm
• 40 cm
• 60 cm
• 70 cm

Solution

Surface area = 600 We know that, surface area of a cube = 6a² 600 = 6a² a² = 600 ÷ 6 a² = 100 a = 10 Each side of the cube = 10 cm Thus, Perimeter of each face of the cube = 4 x 10 = 40 cm

Q5. To find the area of a polygonal region:

• Use direct formula to find the area
• Divide the region into triangles and quadrilaterals
• Divides the regions into quadrilaterals only
• Divides the regions into triangles only

Solution

Divide the region into triangles and quadrilaterals

Q6. The ratio between the curved surface area and the total surface area of cylinder is 2:5. Then the ratio between the height and radius of cylinder will be:

• 1:1
• 2:3
• 3:2
• 3:5

Solution

For cylinder,

Q7. Two cubes of  edges 12 cm each are joined edge to edge. The volume of the new solid is:

• 3208 cubic cm
• 1860 cubic cm
• 3456 cubic cm
• 3145 cubic cm

Solution

The new solid has volume equal to the volume of the two cubes taken together=(12)³ + (12)³ = 1728 + 1728 = 3456 cubic cm

Q8. A circular well of diameter 3.5 m is dug upto the depth 6 m. The lateral surface area of the well is ______ .

• 66 sq. m
• 86 sq. m
• 76 sq. m
• 96 sq. m

Solution

Lateral surface area of cylinder = = 66 sq. m

Q9. A wire is in the shape of a rectangle of length 28 cm and breadth 12 cm, if the same wire is bent in the shape of a square then the perimeter of square is:

• 80 cm
• 40 cm
• 120 cm
• 100 cm

Solution

The perimeter of square will be same as that of rectangle. Hence, P = 2(28 + 12) = 80 cm

Q10. The parallel sides of a trapezium whose area is 74.52 cm² are 8.4 cm and 12.3 cm respectively. The height of the trapezium is:

• 7.2 cm
• 7.9 cm
• 8.2 cm
• 6.9 cm

Solution

Q11. Perimeter of a rectangle with length 4 cm and breadth 3 cm is:

• 14 cm
• 7 cm
• 21 cm
• 15 cm

Solution

P = 2(4 + 3) = 2 x 7 = 14 cm

Q12. The area of a trapezium shaped field is 480 m², the distance between two parallel sides is 15 m and one of the parallel side is 20 m. The length of the other parallel side is ______ .

• 11 m
• 22 m
• 33 m
• 44 m

Solution

Let the length of other parallel side be L.

Q13. From a cuboid of dimension 4 x 4 x 5 units, cubes of side length 1 unit are cut. Find the number of cubes obtained.

• 20
• 60
• 80
• 50

Solution

Volume of cuboid = 4 x 4 x 5 = 80 units³ Since the volume of one cube is 1 unit³ So the number of cubes is 80.

Q14. Perimeter of an equilateral triangle whose side is 7.5 cm.

• 15 cm
• 23 cm
• 22 cm
• 22.5 cm

Solution

Perimeter = 7.5 + 7.5 + 7.5 = 22.5 cm

Q15. Surface area of a cubical box of side length 2 m without top is given by:

• 18 m²
• 16 m²
• 24 m²
• 20 m²

Solution

Surface area = 5(2)² = 20 m².

Q16. The perimeter of an equilateral triangle with side 5 cm is:

• 20 cm
• 10 cm
• 12 cm
• 15 cm

Solution

Perimeter = 5 x 3 = 15 cm

Q17. The diameter of a cylinder of volume 6160 cu cm and height 10 cm is ... cm.

• 14
• 28
• 21.5
• 12.5

Solution

Q18. The height of the cuboid whose volume and base area are 275 cm³ and 25 cm² respectively is ______ .

• 10 cm
• 11 cm
• 9 cm
• 15 cm

Solution

Volume = 275 cm³ and Area of the base = 25 cm² Thus, Height =

Q19. Surface area of the four walls of a cube is given by:

• 6a²
• 3a²
• 5a²
• 4a²

Solution

Surface area = 4a².

Q20. The area of a rhombus is 54 cm². If length of one of its diagonals is 9 cm, then what is the length of the other diagonal?

• 11 cm
• 12 cm
• 22 cm
• 24 cm

Solution

Q21. The perimeter of a rectangle is 28 cm and its breadth is 6 cm. The length of a rectangle will be:

• 5 cm
• 6 cm
• 7 cm
• 8 cm

Solution

Perimeter = 2(length + breadth) Thus, 28 = 2(length + 6) Length = 8 cm

Q22. Surface area of a cubical box of side length 8 m without top is given by:

• 350 m²
• 280 m²
• 300 m²
• 320 m²

Solution

Surface area = 5(8)² = 320 m²

Q23. A closed cylindrical tank of radius 7 m and height 5 m is made from a sheet of metal. If the breadth of the rectangular sheet is 10 m, then the length of the sheet is ______ .

• 52.7 m
• 52.3 m
• 52 m
• 52.8 m

Solution

Surface area of cylinder = area of rectangular sheet Thus,

Q24. The perimeter of a rectangle is 72 cm. If the length of the rectangle is 20 cm, the breadth of the rectangle is:

• 18 cm
• 16 cm
• 20 cm
• 12 cm

Solution

Perimeter of a Rectangle = 2 x (l + b) 2 x (20 +b) = 72 cm Hence, b = 36 - 20 = 16 cm

Q25. Lateral (Curved) surface area of cylinder with r = 14 cm and h = 3 cm is:

• 260 cm²
• 264 cm²
• 206 cm²
• 246 cm²

Solution

Lateral (Curved) surface area of cylinder =

Q26. The surface area of an open cuboidal box of side x cm is

• 3x²
• 5x²
• 4x²
• 6x²

Solution

The top surface is missing in the cube, hence the answer is the sum of the ara of 5 surfaces = 5a².

Q27. If the surface area and volume of a cylinder are numerically equal, then its radius is:

• 1 unit
• 3 units
• 2 units
• 4 units

Solution

Since, surface area of cylinder = volume of cylinder Thus, r = 2 units

Q28. A plot of land is in the form of a quadrilateral, where one of its diagonal is 230 m long. The two vertices on either side of this diagonal are at a perpendicular distance of 60 m and 70 m from it. The area of the plot of land is

• 14500 sq. m
• 14950 sq. m
• 15000 sq. m
• 15450 sq. m

Solution

Q29. If the total surface area of a cube is 96 sq. cm, then the length of each side of the cube is

• 2 cm
• 4 cm
• 6 cm
• 8 cm

Solution

Q30. Area of a square is 49 cm². Find its perimeter.

• 28 cm
• 14 cm
• 30 cm
• 35 cm

Solution

Area of square = 49 cm² = 7² cm² Therefore, side of square is = 7 cm So the perimeter of square = 7 x 4 = 28 cm

Q31. Surface area of a cuboids with dimension 2 cm x 2 cm x 3 cm without top is:

• 28 cm²
• 32 cm²
• 22 cm²
• 24 cm²

Solution

Surface area = lb + 2(bh + hl) = 4 + 2(6 + 6) = 4 + 24 = 28 cm².

Q32. The edges of two cubes are in the ratio 3:4. So the ratio of their volumes is ______

• 27:128
• 27:16
• 27:64
• 9:64

Solution

Ratio of their volumes = = 27:64

Q33. Area of a rectangle is 40 cm². If its breadth is 10 cm then its length will be:

• 3 cm
• 2 cm
• 4 cm
• 8 cm

Solution

Length of rectangle = = 4 cm

Q34. The perimeter of a regular polygon of n side is given by:

• 2n x (Side length)
• n x (Side length)
• n + (Side length)
• 3n x (Side length)

Solution

Perimeter of a regular polygon of side n is n x (Side length).

Q35. If the area of a parallelogram is 13.25 cm² and its base is 5.3 cm, then the corresponding height of the parallelogram is: 

• 1.35 cm
• 2.5 cm
• 3.3 cm
• 4.25 cm

Solution

Area of parallelogram = base x height

Q36. The area of a rhombus and that of a square are equal. The side of the square is 6 cm. If one of the diagonal of the rhombus is 4 cm, then the length of its other diagonal is ______ .

• 8 cm
• 10 m
• 18 cm
• 15 m

Solution

Area of square = (6)² = 36 sq. cm Area of rhombus = Thus, d = 18 cm

Q37. The volume of cuboid is 400 m³. Find its length if its breadth and height are 5 m and 10 m.

• 4 m
• 6 m
• 8 m
• 10 m

Solution

Q38. If the volumes of two cubes are in the ratio 64: 125, then what is the ratio of the lengths of their edges?

• 8:5
• 4:5
• 2:25
• 4:25

Solution

Q39. A circular park of radius 6 cm has a path all around its perimeter. If the width of the path is 7 cm, then the area of the path is

• 348 sq cm
• 324 sq cm
• 418 sq cm
• 438 sq cm

Solution

Q40. Perimeter of a regular pentagon with side length 7 cm is:

• 30 cm
• 35 cm
• 21 cm
• 28 cm