Question 1204799: In making a type of cap, a factory cuts out circles of materials of diameter 35cm. If the circles are cut out of a roll of material 105cm wide and the length of the roll is 20m.
How many circles can be cut out of the rolls?
A roll of the material costs ₦3,000 and other costs involved in making the caps are as follows:
thread and stiffening ₦3 per cap, labour ₦4 per cap and other costs ₦10 per cap
What is the cost price per cap?
Found 2 solutions by mananth, greenestamps:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! 105*2000= 210000
Area of each circle, r= 17.5 cm
Area = pi*(17.5)^2 = 962.1127
Number of circles = 210000/962.1127 =218circles
OR
105/35 = 3 circles in a column
2000/35 = 57
57*3 = 171
A roll of the material costs ₦3,000 and other costs involved in making the caps are as follows:
thread and stiffening ₦3 per cap, labour ₦4 per cap and other costs ₦10 per cap
218 circles
material cost per cap = 3000/218= 13.76 N
thread and stiffening cost per cap = 3 N
Labor = 4N
other costs per cap= 10 N
Add them up to get the cost per cap
The cost price per cap, considering material and additional costs, is approximately ₦30.76.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
You can't determine the number of circles by dividing the total area of the roll of material by the area of each circle, as the other tutor did. That result would mean every square cm of the roll is being used, which of course it is not.
The width of the roll is exactly enough for three circles side by side: 150/35 = 3.
The length of the roll is enough for 57 rows of circles: 2000/35 = 57.14...
So the number of circles that can be cut from the roll is 57*3 = 171.
It might be that placing the circles in a hexagonal honeycomb pattern would make it possible to get more than 171 circle from a roll. The would allow more rows of circles on the roll. However, with half the rows having three circles each and half having only two, the total number of circles possible from the roll is less than 171.
So 171 circles can be cut from each roll.
Use that figure to answer the remaining questions.
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