Answer :
The weight of the hollow iron pipe is calculated by finding the volume of iron used, and then multiplying it by the density of iron. The correct weight of the pipe is found to be 3.696 kg, hence the correct option is C. 3.696 kg.
The student's question involves calculating the weight of a hollow iron pipe based on its dimensions and the density of iron. To find the weight of the pipe, we first calculate the volume of iron used, which is the difference between the volumes of the outer cylinder and the inner cylinder (formed by the hollow part).
The volume of the outer cylinder (Vouter) is [tex](\pi\times(router)^2\times height)[/tex], and the volume of the inner cylinder (Vinner) is [tex](\pi\times(rinner)^2\times height)[/tex]. The actual volume of iron (Viron) is (Vouter - Vinner).
Given that the outer radius (router) is 4 cm and the thickness is 1 cm, the inner radius (rinner) is 4 cm - 1 cm = 3 cm. The height is the length of the pipe, which is 21 cm.
Calculating the volume of iron (Viron):
Viron = [tex](\pi\times4^2\times21) - (\pi\times3^2\times21)[/tex]
Viron = [tex](\pi\times(16-9)\times21)[/tex]
Viron = [tex](\pi\times7\times21)[/tex]
Viron = [tex](147\pi) cm^3[/tex]
Now we convert the volume of iron into weight. Using the density of iron (7.9 g/cm3), the weight (W) is:
[tex]W = Volume \ of \ iron \times Density \ of \ iron[/tex]
[tex]W= (147\pi\times7.9) g[/tex]
[tex]W= (1161.3\pi) g[/tex]
Since the weight of iron is given as 8 g for the purpose of this problem, we use this value instead of the actual density. Therefore, the weight of the pipe is:
[tex]W = (147\pi) cm^3 \times 8 g/cm^3[/tex]
[tex]W= (1176\pi) g[/tex]
To obtain the weight in kilograms, we convert grams to kilograms:
[tex]W = (1176\pi / 1000) kg[/tex]
W = 3.696 kg (approximately).
Therefore, the correct option is C. 3.696 kg.