Question

12. The diameter of a roller is 80 cm and its
length is 126 cm. It takes 750 complete
revolutions moving once over to level a
garden. Find the area of the garden.​

Answer 1

Given :-

The diameter of a roller = 80 cm

Height of the roller = 126 cm

Number of revolutions taken = 750

To Find :-

The area of the garden.​

Analysis :-

First find the radius by dividing the diameter by two.

Next find the CSA by it's respective formula.

At last, find the area by it's respective formula in substituting number of revolutions and the CSA.

Solution :-

We know that,

• h = Height
• r = Radius
• d = Diameter
• a = Area
• CSA = Curved Surface Area

Finding radius,

$\underline{\boxed{\sf Radius=\dfrac{Diameter}{2} }}$

Given that,

The diameter of a roller = 80 cm

Substituting their values,

$\sf Radius=\dfrac{80}{2} =40 \ cm$

Hence, radius of the roller is 40 cm.

The roller is shaped like a cylinder.

By the formula,

$\underline{\boxed{\sf Curved \ surface \ area= 2 \pi rh}}$

Given that,

Radius of the cylinder = 40 cm

Height of the roller = 126 cm

Substituting their values,

$\sf =2 \times \dfrac{22}{7} \times 40 \times 126$

$\sf =31680 \ cm^{2}$

Therefore, the CSA of the roller is 31680 cm².

By the formula,

$\underline{\boxed{\sf Area \ of \ field=Revolutions \times CSA}}$

Given that,

Number of revolutions = 750

CSA of the roller = 31680 cm²

Substituting them,

Area of the garden = 750 × 31680

Area = 23760000 cm²

Therefore, the area of the garden is 23760000 cm²

Answer 2

Answer:

237600 cm2

Step-by-step explanation:

we know  curved surface area of the  cylinder = 2pirh

here given

radius =80/2=40

length=126

so

2*22/7*126*40*750

44*18*40*750

=237600cm2