### Mensuration - Worksheets

CBSE Worksheet-1

Class 08 - Mathematics (Mensuration)

Class 08 - Mathematics (Mensuration)

General Instructions: All questions are compulsory. Q.1 to Q.2 carries one mark each. Q.3 to Q.7 carries two marks each. Q.8 and Q.9 carries three marks each. Q.10 to Q.12 carries four marks each.

- Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
- Find the volume of a cuboid, where l = b = h
- State true of false:
- On the basis of angle, triangle can be categorized into three parts.
- Adjacent angles of parallelogram are supplementary.
- A cuboid has six faces all of which are rectangles.
- A parallelogram becomes a square when the diagonals are equal and right bisectors of each other.

- Fill Up the following:
- 0.000003 is equal to _________ × 10−6.
- 0.07 × 1010 is equal to _________.
- 2-6 × ___= 23
- _____ - (32)0 = 1

- Match the following:
Column A Column B a. Number of sides in decagon i. Rhombus b. Diagonals are perpendicular ii. Zero c. Equals sides in scalene triangle iii. Parallelogram d. Adjacent angles are supplementary iv. Ten - The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
- Find the area of the quadrilateral.
- Find the volume of cube whose Total Surface Area is 486cm2
- The area of trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the another parallel side.
- Describe how the two given figures are alike and how they are different. Which box has larger lateral surface area ?
- 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 84 cm and length is 1 m.
- Factorize 6x2 + 5x – 6

CBSE Worksheet-1

Class 08 - Mathematics (Mensuration)

Solution

Class 08 - Mathematics (Mensuration)

Solution

- Height of the cuboid

= 5 cm. - We know that a cuboid with l = b = h, is a cube

Hence, Volume of cube = l × l × l = l3 - True
- True
- True
- True

- 3
- 700000000
- 29
- 2

- - iv
- - i
- - ii
- - iii

- Area of the field ABCD = 1/2 × Diagonal × ( Height 1 + Height 2)

= 12 × 21

= 252 m2. - Area of the quadrilateral

× diagonal (PR) × diagonal (SQ)

= 21 cm2 - Total surface area= 6(length)2

486 = 6(side)2

(Side)2= 486/6

(Side)2 = 81cm

Side =9cm

Volume =(side)3

Volume = (9)3

Volume = 729 cm3 - Area of trapezium

∴ 34 = 2 × (10 + b)

∴ 10 + b = 17

∴ b = 17 – 10

∴ b = 7 cm

Hence, the length of another parallel side is 7 cm. - Similarity → Both have same heigths.

Difference → One is cylinder, the other is a cube.

For first figure

h = 7 cm

∴ Lateral surface area

= 154 cm2

For second figure

l = 7 cm

b = 7 cm

h = 7 cm

∴ Lateral surface area = 4l2

= 4 × (7)2

= 196 cm2

Hence, the second box has the larger lateral surface area. - Diameter of the road roller = 84 cm

∴ Radius (r) of the road roller cm = 42 cm

Length (h) of the road roller = 1 m = 100 cm

∴ Lateral surface area of the road roller

= 26400 cm2

∴ Area of the road covered in 1 complete revolution = 26400 cm2

∴ Area of the road covered in 750 complete revolutions

= 26400 cm2 × 750 cm2

= 19800000 cm2

= 1980 m2. - Clearly, 9 +( - 4) =5 and 9× - 4 = - 36 . So, we replace the middle term 5x by 9x, – 4x .

Thus we have,

6x2 + 5x – 6 = 6x2 + 9x – 4x – 6

= 3x(2x + 3) – 2 (2x + 3)

= (2x + 3) (3x – 2)