A tin full of melon with a radius of 1.5cm cost 10naira. How much would a similar tin with radius 4.5cm cost
First, we need to calculate the volume of the two tins using the formula for the volume of a cylinder:
V = πr^2h
The volume of the tin with radius 1.5cm is:
V1 = π(1.5)^2h = 2.25πh
Since the tins are similar, the ratio of their volumes is equal to the square of the ratio of their radii:
V2/V1 = (4.5/1.5)^2 = 3^2 = 9
So, the volume of the tin with radius 4.5cm is:
V2 = 9V1 = 9 * 2.25πh = 20.25πh
Now, since the volume of a tin is directly proportional to its cost, we can write the following proportion:
V1 / 10 = V2 / C
Where C is the cost of the tin with radius 4.5cm.
Substitute the volumes we found:
2.25πh / 10 = 20.25πh / C
Simplify the equation:
0.225 = 20.25 / C
C = 20.25 / 0.225
C ≈ 90
So, a similar tin with a radius of 4.5cm would cost approximately 90 naira.