A round carpet with a diameter of 3.6 m was laid on the floor in a rectangular room with sides of 6.2 m and 4.1 m.

A round carpet with a diameter of 3.6 m was laid on the floor in a rectangular room with sides of 6.2 m and 4.1 m. Compare the area occupied by the carpet with the area of the free part of the floor (n = 3.1).

1) Calculate the floor area by multiplying its length and width:

6.2 * 4.1 = 25.42 m ^ 2.

2) Find the area of the carpet.

The area of a circle (S) is calculated by the formula:

S = n * R ^ 2, where n is the number “pi” (n = 3.1), R is the radius of the circle.

R = D: 2, where D is the diameter of the circle.

Then the area of the carpet will be:

3.1 * (3.6: 2) ^ 2 = 3.1 * 1.8 ^ 2 = 3.1 * 3.24 = 10.044 m ^ 2.

3) Find out the floor area not occupied by the carpet:

25.42 – 10.044 = 15.376 m ^ 2.

4) Compare the area occupied by the carpet with the area of the free part of the floor:

10.044 <15.376, which means that the floor area occupied by the carpet is less than the free area.