#### 9-std Mensuration Important Question

9th Standard

Reg.No. :
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Maths

Time : 02:30:00 Hrs
Total Marks : 80
10 x 1 = 10
1. The area of a triangle whose sides are a, b and c is

(a)

$\sqrt { \left( s-a \right) \left( s-b \right) \left( s-c \right) }$sq. units

(b)

$\sqrt { s\left( s-a \right) \left( s-b \right) \left( s-c \right) }$sq. units

(c)

$\sqrt { s\left( s\times a \right) \left( s\times b \right) \left( s\times c \right) }$sq. units

(d)

$\sqrt { s\left( s-a \right) \left( s-b \right) \left( s-c \right) }$ sq. units

2. The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is

(a)

60 cm

(b)

45 cm

(c)

30 cm

(d)

15 cm

3. If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the area is

(a)

3 cm2

(b)

6 cm2

(c)

9 cm2

(d)

12 cm2

4. The total surface area of a cuboid is

(a)

4a2 sq. units

(b)

6a2 sq. units

(c)

2(l + b)h sq. units

(d)

2(lb + bh + lh) sq. units

5. The lateral surface area of a cube of side 12 cm is

(a)

144 cm2

(b)

196 cm2

(c)

576 cm2

(d)

664 cm2

6. If the lateral surface area of a cube is 600 cm2, then the total surface area is

(a)

150 cm2

(b)

400 cm2

(c)

900 cm2

(d)

1350 cm2

7. The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is

(a)

280 cm2

(b)

300 cm2

(c)

360 cm2

(d)

600 cm2

8. The volume of a cuboid is 660 cm3 and the area of the base is 33 cm2. Its height is

(a)

10 cm

(b)

12 cm

(c)

20 cm

(d)

22 cm

9. The capacity of a water tank of dimensions 10 m × 5 m × 1.5 m is

(a)

75 litres

(b)

750 litres

(c)

7500 litres

(d)

75000 litres

10. The number of bricks each measuring 50 cm × 30 cm × 20 cm that will be required to build a wall whose dimensions are 5 m × 3 m × 2 m is

(a)

1000

(b)

2000

(c)

3000

(d)

5000

11. 15 x 2 = 30
12. Using Heron’s formula, find the area of a triangle whose sides are
(i) 10 cm, 24 cm, 26 cm (ii) 1.8 m, 8 m, 8.2 m

13. The perimeter of a triangular plot is 600 m. If the sides are in the ratio 5:12:13, then find the area of the plot

14. An advertisement board is in the form of an isosceles triangle with perimeter 36m and each of the equal sides are 13 m. Find the cost of painting it at Rs.17.50 per square metre.

15. Find the area of the unshaded region.

16. A park is in the shape of a quadrilateral. The sides of the park are 15 m, 20 m, 26 m and 17 m and the angle between the first two sides is a right angle. Find the area of the park.

17. A land is in the shape of rhombus. The perimeter of the land is 160 m and one of the diagonal is 48 m. Find the area of the land.

18. The parallel sides of a trapezium are 15 m and 10 m long and its non-parallel sides are 8 m and 7 m long. Find the area of the trapezium.

19. The dimensions of a hall is 10 m × 9 m × 8 m. Find the cost of white washing the walls and ceiling at the rate of Rs.8.50 per m2.

20. A cubical container of side 6.5 m is to be painted on the entire outer surface. Find the area to be painted and the total cost of painting it at the rate of Rs.24 per m2.

21. The length, breadth and height of a chocolate box are in the ratio 5:4:3. If its volume is 7500 cm3, then find its dimensions.

22. The dimensions of a brick are 24 cm × 12 cm × 8 cm. How many such bricks will be required to build a wall of 20 m length, 48 cm breadth and 6 m height?

23. Th e volume of a container is 1440 m3. Th e length and breadth of the container are 15 m and 8 m respectively. Find its height.

24. If the total surface area of a cube is 726 cm2, then find its volume.

25. A cubical milk tank holds 125000 litres of milk. Find the length of its side in metres.

26. External dimensions of a closed wooden cuboidal box are 30 cm ×25 cm ×20 cm. If the thickness of the wood is 2 cm all around, find the volume of the wood contained in the cuboidal box formed.

27. 10 x 3 = 30
28. The lengths of sides of a triangular field are 28 m, 15 m and 41 m. Calculate the area of the field. Find the cost of levelling the field at the rate of ₹ 20 per m2

29. Find the TSA and LSA of a cuboid whose length, breadth and height are 7.5 m, 3 m and 5 m respectively.

30. A closed wooden box is in the form of a cuboid. Its length, breadth and height are 6 m, 1.5 m and 300 cm respectively. Find the total surface area and cost of painting its entire outer surface at the rate of $\triangle$50 per m2.

31. The length, breadth and height of a hall are 25 m, 15 m and 5 m respectively. Find the cost of renovating its floor and four walls at the rate of $\triangle$80 per m2.

32. Two identical cubes of side 7 cm are joined end to end. Find the total surface area and lateral surface area of the new resulting cuboid.

33. The length, breadth and height of a cuboid is 120 mm, 10 cm and 8 cm respectively. Find the volume of 10 such cuboids.

34. The dimensions of a fish tank are 3.8 m × 2.5 m × 1.6 m. How many litres of water it can hold?

35. The dimensions of a sweet box are 22 cm × 18 cm × 10 cm. How many such boxes can be packed in a carton of dimensions 1 m × 88 cm × 63 cm?

36. Find the volume of cube whose side is 10 cm.

37. A cubical tank can hold 64,000 litres of water. Find the length of its side in metres.

38. 2 x 5 = 10
39. Find the area of a quadrilateral ABCD whose sides are AB = 8cm, BC = 15 cm, CD = 12 cm, AD = 25 cm and = 90°.

40. A farmer has a field in the shape of a rhombus. The perimeter of the field is 400 m and one of its diagonal is 120 m. He wants to divide the field into two equal parts to grow two different types of vegetables. Find the area of the field.