Answer:
The volume of the large can is equal to the volume of 8 small cans.
Step-by-step explanation:
The tomato can has a cylinder format, and the volume of a cylinder is calculated multiplying the base area by the height.
The base area is the area of a circle, which is pi*r^2, where r is the radius.
If the radius increases by 2 times, the base area increases by 4 times, as the base area has r^2 in its formula.
If the height increases by 2 times, the volume of the cylinder also increases by 2 times.
So, in total, the volume of the large can is 8 times the volume of the small can, that is, the volume of the large can is equal to the volume of 8 small cans.
We can also solve this problem using the formulas:
V = A*h, where V is the small can volume, A is the base area of the small can, and h is the height of the small can.
A = pi*r^2, where r is the radius of the small can.
h' = 2*h (h' is the height of the large can)
r' = 2*r (r' is the radius of the large can)
A' = pi*(r')^2 = pi*(2r)^2 = pi*4r^2 = 4A (A' is the base area of the large can)
V' = A'*h' = 4A * 2h = 8Ah = 8V (V' is the volume of the large can)
