Final answer:
The total length of brass used to make the girl's neck ring is 840 cm. The radius of the brass is 6.37 cm. The volume of the unwound brass cylinder is 1540.84 cm³. The mass of the brass used to make the neck ring is 13.46 kg.
Step-by-step explanation:
b) To calculate the total length of brass used to make the girl's neck ring, we need to find the circumference of each turn of the coil and multiply it by the total number of turns. The circumference of each turn is 40 cm, and there are 21 turns, so the total length is 40 cm x 21 = 840 cm.
c) To find the radius of the brass, we can use the formula for circumference: C = 2πr. Rearranging the formula, we have r = C / (2π), where C is the circumference of each turn. Plugging in the values, we get r = 40 cm / (2 x 3.142) = 6.37 cm.
d) To find the volume of the unwound brass cylinder, we can use the formula V = πr^2h, where r is the radius of the cylinder (which is the same as the radius of the brass) and h is the height of the coil. Plugging in the values, we get V = 3.142 x (6.37 cm)^2 x 12 cm = 1540.84 cm³.
e) To find the mass of the brass, we can use the formula m = ρV, where ρ is the density of brass and V is the volume of the unwound cylinder. Plugging in the values, we get m = 8.73 g/cm³ x 1540.84 cm³ = 13460.47 g. Since the density is given in g/cm³ and we want the mass in kg, we need to convert grams to kilograms by dividing by 1000. So the mass is 13.46 kg.