A circular room of a radius of 14 m is to be covered by a square carpet. What will be the maximum area the carpet can cover? If the same area is to be paved with square tiles with side length 70 cm, then how many tiles would be needed?
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Step-by-step explanation:
The square carpet covers limited area inside the circular room.
The diameter and the diagonal of the square is equal.
Since the radius of the room is 14 m; diameter is 28 m
Diagonal of the square carpet splits the square into 2 triangles.
Radius = height of the triangles and
diameter = base of the triangle
since there are 2 triangles:
2*1/2 *b* h
cancelling the 2 from the numerator and the denominator
leaving the b*h
= 28 * 14
= 392 m^2
converting it to cm
= 392 * 100 * 100
= 3920000 cm^2
The side of the square tile = 70cm
Area of the tile = 70 * 70
= 4900 cm^2
number of required tiles = 3920000/4900
= 800
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