a rope 60m long and 5cm in diameter is coiled tightly. Estimate, correct to one significant figure, the radius of the 'circle' formed. ( please could we have working out).
The lateral surface area of the rope is 60m*5cm = 6000cm*5cm = 30,000 cm².
A circle with the same area and radius r is
πr² = 30000
Solve for r to get
r=sqrt(30000/π)=98 cm, or 0.98 m.
or 1 m to one significant figure.
To estimate the radius of the circle formed by the tightly coiled rope, we can assume that each coil of the rope forms a circle. We need to find the number of coils in the rope.
The length of the rope is 60m, and we can calculate the circumference of each coil using the formula:
Circumference = 2 * π * radius
Since the diameter of the rope is given as 5cm, the radius is half of that, which is 2.5cm or 0.025m.
Now, we can divide the total length of the rope by the circumference of each coil to find the number of coils:
Number of coils = Total length of rope / Circumference of each coil
Number of coils = 60m / (2 * 3.14 * 0.025m)
Number of coils ≈ 60m / (0.157m)
Number of coils ≈ 382.17
Since the number of coils must be a whole number, we round down to the nearest whole number to get:
Number of coils ≈ 382
Now, since each coil forms a circle, we can estimate the radius of the circle formed by dividing the length of the rope by the number of coils:
Estimated radius ≈ Total length of rope / Number of coils
Estimated radius ≈ 60m / 382
Estimated radius ≈ 0.157m
Therefore, the estimated radius of the circle formed by the tightly coiled rope is approximately 0.2m (rounded to one significant figure).
I don't know answer
To estimate the radius of the "circle" formed by the tightly coiled rope, we can use the formula for the circumference of a circle, which is:
C = 2πr
where C is the circumference of the circle and r is the radius.
In this case, the given information is the length of the rope, which is equal to the circumference of the circle when it is tightly coiled. The length of the rope is given as 60m.
60 = 2πr
To find the radius, rearrange the equation to solve for r:
r = 60 / (2π)
Now we can calculate the radius:
r ≈ 60 / (2 × 3.14)
r ≈ 60 / 6.28
r ≈ 9.55
Therefore, the radius of the "circle" formed by the tightly coiled rope is approximately 9.55m when rounded to one significant figure.