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Radius of the round carpet = 63 cm 

Area covered by the round carpet = πr² sq units

A = \(\frac{22}{7}\) x 63 x 63 

= 22 x 9 x 63 

= 12474 cm² 

Area covered by the round carpet = 12,474 cm²

Diameter of the circular table cover = 3m 

Circumference C = πd units 

= 3.15 x 3 m 

= 9.45 m 

Length of the lace required = 9.45 m 

Cost of lace per meter = Rs 30 

∴ Cost of 9.45m lace = Rs 30 x 9.45 = Rs 283.50

Radius of the circular swimming pool r = 7 m 

Area of the circular swimming pool A = πr² sq. units 

= \(\frac{22}{7}\) x 7 x 7 m² 

= 154 m² 

Cost of cementing a m² floor = Rs 18. 

Cost of cementing 154 m² floor = Rs 18 x 154

= Rs 2,772

Area of the circle = πr² sq.units 

Area of the circular portion watered = 1386 cm² 

πr² = 1386 

\(\frac{22}{7}\) x r² = 1386

r² = 1386 x \(\frac{7}{22}\)

= 63 x 7 

= 9 x 7 x 7 

r² = 3² x 7² 

r = 3 x 7 

Radius (r) = 21 cm

Diameter (d) = 2r 

= 2 x 21 cm 

Diameter (d) = 42 cm

Diamter of the circular garden d = 49 m 

Radius r = \(\frac{d}{2}\)

= \(\frac{49}{2}\) m

Area of the circular garden = πr² sq units 

= \(\frac{22}{7}\) x \(\frac{49}{2}\) x \(\frac{49}{2}\) m²

= 1,886.5 m² 

Cost of levelling a m² area = Rs 150 

∴ Cost of levelling 1886.5 m² = Rs 150 x 1886.5 

= Rs 2,82,975 

Cost of levelling the flower garden = Rs 2,82,975

The SI unit of electric charge is Coulomb (C)

Correct answer is (b) kg/m³

SI unit of speed m/s.

The known measure of a physical quantity is called the unit of measurement.

Given : Density Copper Dc = 8900 kg/m³

Density of Iron D₁ = 7800 kg/m³ 

Volume of Copper sphere = Volume of Iron sphere

To find : Ratio of Masses of Copper (M_C) and Iron (M_I)

Solution: Mass = Density x Volume 

M_C = D_C x V, M₁ = D₁ x V 

M_C = 8900 V, M₁ = 7,800 V 

M_C = M₁ 

8900 V : 7800 V 

= 1.14: 1

Comparison of an unknown quantity with a standard quantity is called measurement.

Given : radius of a sphere r = 1cm 

Volume of the sphere V = ? 

Mass of the sphere M = 33 g 

Density of silver D = ?

Density D = \(\frac{Mass\, of\,the \,sphere\,(M)}{Volume\,of \, the\,sphere (V}\)

Solution: Density of silver sphere = 7.889 g/cc

Area is the measure of the region inside a closed line.

Iron needle is compact and its density is 7.6 g/cm³ Thus, as the density of iron needle is more than 1 g/cm³ therefore, it sinks in water. However, the iron ship is constructed in such a way that it is mostly hollow from within, thus, the volume of iron ship becomes very large as compared to its mass and hence its density is less than 1g/cm³ . As the density of iron ship is less than 1g/cm³ , therefore it floats in water.

Gallon, ounce and quart

Wooden block.

Astronomical unit and light year are the units used to measure the distance between celestial objects.

Correct answer is (c) area

1. (False) 

Correct statement: The region covered by the boundary of plane figure is called its area.

2. True

3. True

4. True

5. False. 

Correct statement: A substance which contains more number of molecules per unit volume is said to be denser.

Volume of a cylinder = πr² h

(a) Both A and R are true but R is not the correct reason.

Correct answer is (a) Distance

One light year = 9.46 x 10¹⁵ m

Iron ball sinks in water. The density of an iron ball is more than that of water so it sinks in water.

Correct answer is (b) 2:1

The fundamental unit of amount of substance is mole (mol)

1. c 

2. d 

3. e 

4. b 

5. a

Given :The dimension of a school 

Playground = l x b = 800 m x 500 m 

Formula :Area of the ground A = l x b 

= 800 x 500 = 4,00,000 

A = 4,00,000 m²

A set of physical quantities which cannot be expressed in terms of any other quantities are known as fundamental quantities. Ex: Length, mass, time.

• The multiples of mass are quintal and metric tonne. 
• The sub-multiples of mass are gram and milligrams.

Given radius = 10 cm = 0.1m 

π= 3.14 

Area of a circular disc A = ? 

Formula : Area of a circle A = πr² 

= 3.14 × 0.1 × 0.1 

Solution : A = 0.0314 m²

1. c 

2. d 

3. a 

4. b

Mass is the amount of matter contained in a body. It’s unit is kilogram (kg).

(b) If both assertion and reason are true, but reason is not the correct explanation of assertion 

Correct explanation : Density of iron is more than that of water.

1. i 

2. ii 

3. iii 

4. iv 

5. v

1. M³

2. cm³

3. Iron

(b) If both assertion and reason are true, but reason is not the correct explanation of assertion 

Correct explanation: Density of water is more than the density of wood.

(a) length × breadth

Density of gold is 19,300 kg/m³

1. i 

2. ii 

3. iii 

4. iv 

5. v

n × r² = πr²

One astronomical unit is defined as the average distance between the earth and the sun. 1AU = 1.496 x 10¹¹ m or 149.6 x 10⁶ m

One astronomical unit is defined as the average distance between the earth and the sun.

1 AU = 1.496 x 10⁵ x 10⁶ km = 1.496 × 10¹¹ m.

1. 10 cc, 100 cc, 1L, 10L

2. Aluminium, Iron, Copper, Gold

(a) If both assertion and reason are true and reason is the correct explanation of assertion

Density (D) = \(\frac{mass(m)}{volume (v)}\)

D = \(\frac{(m)}{(v)}\)

Graphical method

One light year is the distance travelled by light in vacuum during the period of one year. 

1 Light year = 9.46 x 10¹⁵ m.

V₁ = 30 cc, V₂ = 40 cc; Volume of stone =v₂ – v₁ 

= 40cc – 30cc = 10cc

(d) 1L = 1000cc