Use a chart paper of length 40 cm and breadth 5 cm to draw circles of ...
Introduction:
In this problem, we are given a chart paper with a length of 40 cm and a breadth of 5 cm. We need to draw circles of radius 2.5 cm on the chart paper in such a way that they touch each other. We have to determine the number of circles that can be drawn in this arrangement.
Key Information:
- Length of the chart paper: 40 cm
- Breadth of the chart paper: 5 cm
- Radius of the circles: 2.5 cm
- Circles should touch each other
Approach:
To find the number of circles that can be drawn, we need to calculate the maximum number of circles that can fit in the given space without overlapping or leaving any gaps.
Calculating the number of circles:
To calculate the number of circles that can be drawn, we need to consider the space available on the chart paper and the space occupied by each circle.
Space occupied by each circle:
The diameter of each circle is twice the radius, so the diameter of each circle is 2 * 2.5 cm = 5 cm.
Calculating the number of circles in length:
The length of the chart paper is 40 cm, and the diameter of each circle is 5 cm. Therefore, the maximum number of circles that can be accommodated in the length is 40 cm / 5 cm = 8.
Calculating the number of circles in breadth:
The breadth of the chart paper is 5 cm, and the diameter of each circle is 5 cm. Therefore, the maximum number of circles that can be accommodated in the breadth is 5 cm / 5 cm = 1.
Calculating the total number of circles:
To calculate the total number of circles, we multiply the number of circles in length by the number of circles in breadth. So, the total number of circles that can be drawn is 8 * 1 = 8.
Conclusion:
In conclusion, we can draw a total of 8 circles on the given chart paper of length 40 cm and breadth 5 cm. Each circle has a radius of 2.5 cm and they touch each other. The maximum number of circles that can be accommodated in the length is 8, and the maximum number of circles that can be accommodated in the breadth is 1. Therefore, the total number of circles that can be drawn is 8.
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