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Given:

Dimension of smaller rectangular plot = 40 × 60

Dimension of larger rectangular plot = 120 × 160

Calculation:

Area of smaller rectangular plots = (40 × 60) m²

⇒ 2400 m²

Area of larger rectangular plots = (120 × 160) m²

⇒ 19200 m²

Number of rectangular plots which can be made = (19200 m²/2400 m²)

⇒ 8

∴ The required number of rectangular plots is 8

Given:

The diameter of the semicircular sheet is 56 cm

Concept Used:

If a semicircular metal bent in the shape of a conical bowl then the slant height of the cone will be same as the radius of the semicircle.

Calculation:

The diameter of the semicircle is 56 cm

The radius of the semicircle (r) = 28 cm

That means the slant height of the cone (l) = 28 cm also

The length of the semicircular sheet is πr

⇒ (22/7) × 28

⇒ 88 cm

That means the circumference of the base of the cone is also 88 cm

Let the radius of the base of the cone is r₁

2πr₁ = 88

⇒ 2 × (22/7) × r₁ = 88

⇒ r₁ = 14

The radius of the base of the conical bowl (r₁) = 14 cm

Let, the height of the cone is h

h = √(l² – r₁²)

⇒ h = √(28² – 14²)

⇒ h = √(784 – 196)

⇒ h = √588

⇒ h = 14√3

∴ The depth of the bowl is 14√3 cm.

Given 

Length of rectangle = 12 cm 

Width of rectangle = 8 cm 

Formula used 

Area of rectangle = length × breadth

Total surface area of cube = 6(side)²

Calculation 

⇒ Area of rectangle = surface area of cube 

⇒  12 × 8 = 6 × side²

⇒  side of cube = 4 cm 

∴ the side of the cube is 4 cm 

Given:

Perimeter of the square = 44 cm

Perimeter of square = Circumference of the circle

Formula used:

Circumference of the circle = 2πr

Area of the circle = πr² 

Calculation:

As, Perimeter of square = Circumference of the circle

⇒ 44 = 2πr 

⇒ r = 7 cm

Area of the circle = πr² 

⇒ Area of the circle = (22/7) × 7² 

∴ Area of the circle is 154 cm² 

Mensuration is a subject or branch of Mathematics.

Mensuration tells us about the lengths of sides, heights and perimeters, measures of angles, surface areas and volumes of 2-dimensional plates and 3-dimensional solids.

 Examples of different shapes are triangle, square, polygon, cylinder, cone, pyramid, cuboid etc.

Some of the real life applications are:-

• Amount of paint required to cover a certain surface area
• Amount of carpet required for a particular room
• Fencing needed for the perimeter of a garden
• Pavement tessellation of a pathway
• Volume of soil needed to fill in a ditch
• The distance around a circular race track
• Travel and roadmap reading
• Amount of fuel needed for a given journey
• Gift wrapping 
• Finding capacities of containers, tanks etc.

Given: 

Radius of base = 7 meter

Height = 5 meter

Formula Used:

Volume of cylinder = πr2h

Where r = radius and h = height of the cylinder

Calculation:

The capacity of cylindrical tank = (22/7) × 7² × 5 meter³

⇒ 22 × 7 × 5 meter³

⇒ 110 × 7 meter³

⇒ 770 meter³

∴ The capacity of the cylindrical tank is 770 meter³

Given:

Radius of cylinder = 21 cm

Height of cylinder = 9 cm

Formula Used:

Total surface area of cylinder = 2πr(h + r)

Where, r = Radius and  h = height of cylinder

Calculation:

Total surface area of cylinder = 2 × 22/7 × 21(9 + 21) cm²

⇒ 2 × 22/7 × 21(30) cm²

⇒ 2 × 22/7 × 630 cm²

⇒ 44 × 90 cm²

⇒ 3960 cm²

∴ The total surface area of the cylinder is 3960 cm²