Identical cylindrical tins of diameter 10cm height of 20cm and a mass of 20g each packed into the box calculate maximum number of tins that can be packed
b) the total mass of box and tins in kg
To calculate the maximum number of tins that can be packed, we need to determine the volume of both the box and the tins.
The volume of a cylinder is given by the formula:
V = πr^2h
Where V is the volume, r is the radius, and h is the height.
Given that the diameter of the tins is 10cm, the radius (r) can be found by dividing the diameter by 2:
r = 10cm / 2 = 5cm = 0.05m
The height of each tin is given as 20cm = 0.2m.
The volume of each tin can be calculated as:
V_tin = π(0.05m)^2(0.2m) = 0.005π m^3
Now, we need to determine the volume of the box. Since the box is not specifically defined, we will assume it to be a rectangular prism with dimensions larger than the tins.
Let's say the dimensions of the box are L x W x H. Without further information, we cannot determine the exact dimensions of the box. However, we can still calculate the volume of the box using the formula:
V_box = LWH
To maximize the number of tins packed, we assume that the tins can pack tightly with no wasted space. In that case, the dimensions of the box should be such that they are multiples of the tins' dimensions.
We can see that the dimensions of each tin can fit exactly:
L = 10cm = 0.1m
W = 10cm = 0.1m
H = 20cm = 0.2m
Now we can calculate the volume of the box:
V_box = (0.1m)(0.1m)(0.2m) = 0.002m^3
To find the maximum number of tins that can be packed, we divide the volume of the box by the volume of each tin:
Max number of tins = V_box / V_tin
= 0.002m^3 / (0.005π m^3)
≈ 127 tins (rounded to the nearest whole number)
Therefore, the maximum number of tins that can be packed is 127.
To calculate the total mass of the box and tins, we multiply the mass of each tin by the number of tins, and convert the mass to kilograms:
Total mass (kg) = (20g)(127) / 1000 = 2.54 kg
Therefore, the total mass of the box and tins is 2.54 kg.