The figure shows a continuous belt passing round two pulleys. The radii of the pulleys are 20 cm and 5 cm, and their centres are 30 cm apart. Assuming that the straight portions of the belt are tangential to the two circles, find the total length of the belt correct to the nearest 0.1 cm
To find the total length of the belt, we need to calculate the circumference of both circles and add them together.
The circumference of a circle is given by the formula C = 2πr, where r is the radius.
For the larger pulley with a radius of 20 cm, the circumference is C1 = 2π(20) = 40π cm.
For the smaller pulley with a radius of 5 cm, the circumference is C2 = 2π(5) = 10π cm.
Since the straight portions of the belt are tangential to the two circles, the total length of the straight portions is equal to the distance between the centers of the two pulleys, which is given as 30 cm.
Therefore, the total length of the belt is the sum of the circumferences of the two circles and the straight portion:
Total length = C1 + C2 + 30 cm
Approximating π to 3.14, we can calculate the total length:
Total length = 40π + 10π + 30 cm
Total length = 50π + 30 cm
Total length ≈ 50(3.14) + 30 cm
Total length ≈ 157 + 30 cm
Total length ≈ 187 cm
Therefore, the total length of the belt is approximately 187 cm.
To find the total length of the belt, we need to consider the circumferences of both pulleys and the distance between their centers.
The circumference of a circle is calculated using the formula:
Circumference = 2 * π * radius
For the larger pulley with a radius of 20 cm:
Circumference1 = 2 * π * 20 cm
For the smaller pulley with a radius of 5 cm:
Circumference2 = 2 * π * 5 cm
To find the length of the belt for the straight portion between the pulleys, we need to calculate the distance between their centers. Given that the centers are 30 cm apart:
Straight portion length = 2 * 30 cm = 60 cm
Finally, we can calculate the total length of the belt by summing the circumferences of both pulleys and the length of the straight portion:
Total length = Circumference1 + Circumference2 + Straight portion length
Total length ≈ (2 * π * 20 cm) + (2 * π * 5 cm) + (60 cm)
Calculating the above expression, we get:
Total length ≈ 125.6 cm + 31.4 cm + 60 cm
Total length ≈ 217 cm
Therefore, the total length of the belt is approximately 217 cm, correct to the nearest 0.1 cm.