** NUMERICALS:**

1. The length, breadth and height of a water tank are 5 m, 2-5 m and 1-25 m respectively. Calculate the capacity of the water tank in (a) m^{3} b) liter.

Ans: Given L= 5 m , B= 2.5 m, H= 1.25 m

V= LxBxH

= 5 m x 2.5 m x 1.25 m = 15.625 m³

= 15625 liter. ( 1 m³ = 1000 liter)

2. A solid silver piece is immersed in water contained in a measuring cylinder. The level of water rises from 50 mL to 62 mL.. Find the

Ans: Given V1= 50 ml, V2= 62 ml

Volume of silver piece= amount of water displaced

= V2- V1 = 62-50 cm³= 12 cm³

3. Find the volume of a liquid present in a dish of dimensions 10 cm x 10 cm x 5cm

Ans. Given Dimension of dish = 10 x 10 x 5 cm³

Volume of water= 10 x 10 x 5 mL

= 500 mL.

4. A rectangular field is of length 60 m and breadth 35 m. Find the area of the field.

Ans. Given L= 60 cm , B = 35 cm

A = L x B

= 60 x 35 cm² = 2100 m²

6. A piece of brass of volume 30 cm³ has a mass of 252 g. Find the density of brass in (i)g/cm³ (ii) kg/ m³

Ans. Given M = 252 g , V = 30 cm³ (i) D = M/ V = 252 / 30 = 8.4 g / cm³

(ii) as 1 g / cm³ = 100 kg/ m³

8.4 g/ cm³ = 8400 kg / m³

7. The mass of an iron ball is 312 g. The density of iron is 7.8 g/cm³ . Find the volume of the ball.

Ans. Given , M= 312 g , D = 7.8 g/ cm³V= M/ D

= 312 / 7.8 g/ cm³ = 40 g / cm³

8. A cork has a volume 25 cm³ . The density of cork is 0.25 g / cm³ . Find the mass of the cork. Ans. Given, V= 25 cm³ , M = ? , D = 0.26 g/ vm³M = V x D = 25 cm³ x 0.25 g/ cm³

= 6.25 g

9. The mass of 5 liter of water is 5 kg. Find the density of water in g / cm³.

Ans. Given, V = 5 liter = 5000 cm³

M = 5 kg = 5000 g

D = M / V = 5000 g / 5000 cm³ = 1 g / cm³

10. A cubical tank of side 1 m is filled with 800 kg of a liquid. Find: (i) the volume of tank, (ii) the density of liquid in kg / m³. Ans. Given, M = 800 kg , side = 1 m (i) volume= side x side x side = 1 x 1 x 1 m³= 1 m³

(ii) density of liquid= M/ V = 800 kg / 1 m³

= 800 kg/ m³

11. A block of iron has dimensions 2 m x 0.5 m x 0.25 m. The density of iron is 7.8 g/cm³ Find the mass of block.

Find: (i) the volume of the lead piece, ii) the density of the lead in kg/ m³

Ans. Given, V = dimensions 2 m x 0.5 m x 0.25 m

= 0.25 m³

D = 7.8 g/ cm³ = 7800 kg/ m³

M= DxV = 7800 x 0.25 m³ = 1950 kg

12. The mass of a lead piece is 115 g . When it is immersed into measuring cylinder, the water level rises from 20 mL mark to 30 mL mark Find :- i) the volume of the lead piece is) the density of the lead in kg / m³.

Ans. V= final volume - initial volume =( 30 - 20 ) mL= 10 mL

13. The density of copper is 8.9 g/ cm³ What be its density in kg/ m³?

Ans. As 1 g/ cm³ = 1000 kg/ m³

8.9 g/ cm³ = 8.9 x 1000 kg/ m³ = 8900 kg/ m³

14. A car travels a distance of 15 km in 20 min Find the speed of the car in (i) km / h ii) m/s

Ans. Given , distance= 15 km , time = 20 min = 20/60 s = 1/3

Speed = distance ÷ time

= 15 ÷ 1/3 = 15 x 3 = 45 km/ h = 45 x 5/18 = 12.5 m/s

15. How long a train will take to travel a distance 200 km with a speed of 60 km/ h ?

Ans. Given, distance= 200 km , speed = 60 km/ h

Time = distance ÷ speed

= 200 km ÷ 60 km/ h = 10/ 3 = 3 h 20 min

16. A boy travels with speed of 10 m / s in 30 minute. How much distance does he travel ?

Ans. Distance= speed x time = 10 x 180 m

= 1800 m/s

17. Express 36 km/ h in m s¹,

Ans. 36 km/ h = 36 x 5/18 m /s = 10 m/s

18. Express 15 m/s in km/ h

Ans,

15 x 18/5 = 54 km

** SHORT ANSWER TYPE QUESTIONS**:

1. Define the term volume of an object.

Ans. The space occupied by an object is called it's volume.

2. State and define the S.L. unit of volume.

Ans. S.I unit of volume is m³.

Volume of a cube is said to be one m³ if it's each side is 1 m.

3. State two smaller units of volume. How are they related to the S.1. unit ?

Ans. Two units of volume are cm³ and dm³

1 m³ = 1000000 cm³

1 m³ = 10000000000 dm³

4. How will you determine the volume of a cuboid? Write the formula you will use.

Ans. To find volume of a cuboid , its length, breadth and height measured by using ruler.

Formula for Volume= length x breadth x height is used to calculate ii ts volume

5. You are required to take out 200 ml. of milk from a bucket full of milk. How will you do it ?

Ans. To take out 200 ml of milk from a bucket full of milk, measuring breaker of 200 ml required.

6. Define the term density of a substance.

Ans. Density of a substance is mass of a body per unit its volume.

7. State the S.L. and C.GS. units of density. How are they related ?

Ans. S.I unit kg/ m³

C GS unit g/ cm³

1 kg/ m³ = 1000 g ÷ 1000000 cm³

= 1/ 1000 g/ cm³

Or 1 g/ cm³= 1000 kg/ m³ of

8. 'The density of brass is 8.4 g/cm³ . What do you mean by the statement?

Ans. It means mass of 1 cm³ volume of brass is 8.4 g.

9. Arrange the following substances in order of their increasing density:

(b) cork

(c) brass

(a) iron

d) water

(e) mercury.

Ans. Cork, water, iron, brass , mercury

10. How does the density of water change when:

(a) it is heated from 0°C to 4°C.

(b) it is heated from 4°C to 10 °C ?

Ans. a) it is heated from 0°C to 4°C- density increases

(b) it is heated from 4°C to 10 °C- decreases

11. Write the density of water at 4°C.

Ans. The density of water at 4°C is 1 g/ cm³= 1000 kg/ m³

12. Explain the meaning of the term speed.

Ans. Distance covered per unit time.

13. Write the S.I. unit of speed.

Ans. S.I. unit of speed - m/s

14. A car travels with a speed 12m/s, while a scooter travels with a speed 36 km /h. Which of the two travels faster ?

Ans:- A car , 12m/s

Scooter 36 km/ h = 36x 5/18 = 10 m/s

Car travel faster.

** LONG ANSWER TYPE QUESTIONS**:

1. Name two devices which are used to measure the volume of an object. Draw their neat diagrams.

Ans:- Two devices - Measuring cylinder and Measuring breaker.

2. How can you determine the volume of an irregular solid (say a piece of brass)? Describe in steps with neat diagrams.

Ans:- To measure the volume of a piece of brass. Take a piece of brass, a measuring cylinder, fine thread of sufficient length and some water. Place a measuring cylinder on a flat horizontal surface and fill it partially with water. Note the reading V₁ of the water level very carefully. Now tie the piece of brass with a thread and dip it completely into water . We see that the level of water rises. Note the reading V₂ of the new water level. Difference in the two levels of water gives the volume of the piece of brass piece

Initial level of water V₁

Level of water when brass piece is immersed V₂

Volume of water displaced =(V₂-V₁) ml

Volume of brass piece= (V₂-V₁) cm³

3. Describe the method in steps to find the area of an irregular lamina using a graph paper.

Ans:- Place an irregular object on a graph sheet. Draw an outline of the object and remove it. First, count the number of complete squares. Then, count the number of incomplete squares which are half and more than half (within the outline). Ignore the squares which are less than half (within the outline). The sum of the areas of the number of complete squares and the number of incomplete squares gives the approximate area of the irregular object.