Question

The length of the roller is 40 cm and 21 cm it takes 300 complete relation to move once over to level a floor of a room find the area of the room in metres square

Answer 1

Answer:

length:40cm

diameter:20cm

radius:21/2=10.5

∆SA=2πrh

=2×12/4×10.5×40

=2640cm²

Area of the room=∆SA×revolutions

=2640×300

=792000cm²

=79.2m² Answer

Step-by-step explanation:

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Answer 2

Question:

The length of the roller is 40 cm and diameter is 21 cm. It takes 300 revolutions to move once over to level a floor of a room. Find the area of the room in m².

Answer:

Area of the room = 79.2 m²

Step-by-step explanation:

Given:

• Length of the roller (height) = 40 cm = 0.4 m
• Diameter of the roller = 21 cm = 0.21 m
• Revolutions taken to move once over to level the room = 300

To Find:

• Area of the room

Concept:

First find the lateral surface area of the roller and the area covered by it in one revolution. Multiplying the area covered in one revolution by number of revolutions gives us the area of the  room.

Solution:

Here the roller is in the shape of a cylinder.

The radius of the cylinder = diameter/2

Radius of cylinder = 0.21/2

First we have to find the curved surface area of the cylinder.

CSA of a cylinder is given by,

CSA of a cylinder = 2 π r h

Substitute the data,

CSA of the cylinder =  2 × 22/7 × 0.21/2 × 0.4

CSA of the cylinder = 22 × 0.03 × 0.4

CSA of the cylinder = 0.264 m²

Hence area of the roller is 0.264 m²

Now,

Area covered in 1 revolution = Area of roller

Area covered in 1 revolution = 0.264 m²

Also,

Area of the room = Area covered in 1 revolution × Number of revolutions

Substitute the data,

Area of the room = 0.264 × 300

Area of the room = 79.2 m²

Hence area of the room is 79.2 m²