At a grocery store, she sees a can of tomato sauce that has a radius and height that are twice that of the small can. The volume of this large can is equal to the volume of how many of the small cans ?

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)

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step-by-step explanation:

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