A circular cloth had 3 rows of lace each 10 centimetres apart around its edge. The radius of the tablecloth was 60 centimetres. how many metres of lace would be needed to decorate the table cloth?
To find the total length of lace needed to decorate the circular cloth, we need to calculate the length of lace required in each row and then multiply it by the total number of rows.
The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius.
In this case, the radius of the tablecloth is given as 60 centimeters. So, the circumference of the circular cloth is:
C = 2π(60) = 120π centimeters.
Now, we know that there are three rows of lace, each 10 centimeters apart around the edge of the cloth. This means that the lace will form three concentric circles on the cloth, each with a radius 10 centimeters larger than the previous one.
To find the length of lace required for each row, we need to calculate the circumference of each of these concentric circles.
For the innermost circle, the radius would be 60 centimeters. So, the circumference of the first row of lace would be:
C1 = 2π(60) = 120π centimeters.
For the second row, the radius would be 70 centimeters. So, the circumference of the second row of lace would be:
C2 = 2π(70) = 140π centimeters.
For the outermost row, the radius would be 80 centimeters. So, the circumference of the third row of lace would be:
C3 = 2π(80) = 160π centimeters.
Now, to find the total length of lace needed to decorate the tablecloth, we simply add the circumferences of all three rows:
Total length of lace = C1 + C2 + C3
= 120π + 140π + 160π
= 420π centimeters.
However, the question asks for the length of lace in meters. Since 1 meter equals 100 centimeters, we need to convert the length of lace from centimeters to meters by dividing it by 100:
Total length of lace in meters = (420π) / 100
= 4.2π meters.
Therefore, approximately 4.2π or 13.18 meters of lace would be needed to decorate the tablecloth.