Question

the diameter of a roller is 84 cm and its length is 1.2 m. it takes 500 complete revolutions to once over the level ground find the area of playground in m^2​

Answer 1

Answer :

• Area of the playground, A = 15840 m²

Explanation :

Given :

• Diameter of the roller, d = 84 cm or 8.4 cm.
• Height of the roller, h = 1.2 m.
• No. of revolutions, n = 500.

To find :

• Area of the playground, A = ?

Knowledge required :

• Curved surface area of a cylinder :

⠀⠀⠀⠀⠀⠀⠀⠀⠀C.S.A = 2πrh

Where :

⠀⠀⠀⠀⠀⠀⠀⠀⠀● r = Radius of the cylinder

⠀⠀⠀⠀⠀⠀⠀⠀⠀● h = Height of the cylinder

⠀⠀⠀⠀⠀⠀⠀⠀⠀● C.S.A. = Curved surface area of the cylinder

• Area of a ground, when the roller and no. of revolution :

⠀⠀⠀⠀⠀⠀⠀⠀A = A' × n

Where,

⠀⠀⠀⠀⠀⠀⠀⠀⠀● A = Area of the ground

⠀⠀⠀⠀⠀⠀⠀⠀⠀● n = No. of revolutions

⠀⠀⠀⠀⠀⠀⠀⠀⠀● A' = Area of the roller

• The value of π = 22/7

• Radius of a circle = Diameter/2

Solution :

⠀⠀⠀⠀⠀⠀⠀⠀⠀Area of the cylinder :

By using the formula for Curved surface area of a cylinder and substituting the values in it, we get :

⠀⠀=> C.S.A. = 2πrh

⠀⠀=> C.S.A = 2 × 22/7 × 8.4/2 × 1.2 [R = d/2]

⠀⠀=> C.S.A = 2 × 22/7 × 4.2 × 1.2

⠀⠀=> C.S.A = 2 × 22 × 0.6 × 1.2

⠀⠀=> C.S.A = 2 × 22 × 6/10 × 12/10

⠀⠀=> C.S.A = 3168/100

⠀⠀=> C.S.A = 31.68

⠀⠀⠀⠀⠀⠀∴ C.S.A. = 31.68 m²

⠀⠀

Hence the curved surface area of the roller is 31.68 m².

⠀⠀⠀⠀⠀⠀⠀⠀⠀Area of the playground :

By using the equation for area of a ground and substituting the values in it, we get :

⠀⠀=> A = A' × n

⠀⠀=> A = 31.68 × 500

⠀⠀=> A = 15840

⠀⠀⠀⠀⠀⠀∴ A = 15840 m²

Therefore,

• Area of the playground, A = 15840 m²

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

The diameter of a roller is 84 cm and its length is 1.2 m. It takes 500 complete revolutions to once over the level ground find the area of playground in m².

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Given \: that}}}}$

• Diameter of the roller is 84 cm
• Height of the roller is 1.2 m
• Number of revolution is 500

${\bigstar}\large{\boxed{\sf{\pink{To \: find}}}}$

• Area of playground in m²

${\bigstar}\large{\boxed{\sf{\pink{Solution}}}}$

• Area of playground = 15840 m²

${\bigstar}\large{\boxed{\sf{\pink{Compulsory \: to \: know}}}}$

$\implies$ Formula of curve surface area of cylinder ➝

$\implies$ 2πrh

$\implies$ Where

$\implies$ $\large\purple{\texttt{r means Radius}}$

$\implies$ $\large\purple{\texttt{h means height}}$

$\implies$ Area of ground when roller nd revolution's number ➝

$\implies$ A¹ × n

$\implies$ Where

$\implies$ $\large\purple{\texttt{a¹ means area of rollers}}$

$\implies$ $\large\purple{\texttt{n means Revolution}}$

$\implies$ π is pie

$\implies$ Value of π is 22/7

$\implies$ Formula of circles radius

$\implies$ Diameter/2

${\bigstar}\large{\boxed{\sf{\pink{Full \: solution}}}}$

Area of the cylinder -

$\mapsto$ Curved surface area {CS.A} = 2πrh

$\mapsto$ C.S.A = 2 × 22/7 × 8.4/2 × 1.2

{We write 8.4/2 bcz Radius is equal to diameter/2 }

$\mapsto$ C.S.A = 2 × 22/7 × 4.2 × 1.2

$\mapsto$ C.S.A = 2 × 22/7 × 0.6 × 1.2

$\mapsto$ C.S.A = 2 × 22/7 × 6/10 × 12/10

$\mapsto$ C.S.A = 3168 / 100

$\mapsto$ C.S.A = 31.68 m²

$\large\green{\texttt{Hence CSA is 31.68 m²}}$

Area of the playground -

$\mapsto$ Area = a¹ × n

$\mapsto$ Area = 31.68 {Finded} × 300

$\mapsto$ Area = 15840 m²

$\large\green{\texttt{Hence area of playground is 15840 m²}}$

@Itzbeautyqueen23

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