Question

A food company makes regular and tall soup cans. the area of the base of both cans is 30 cm2. the volume of the regular can is 270 cm3. the tall can is 2 cm taller. what is the volume of the tall soup can?

Answer 1

The volume of the tall soup can is determined by using the formula for the volume of a cylinder, calculating the radius from the given area, finding the height of the regular can, and then adding 2 cm to that height to find the volume of the tall can.

Step-by-step explanation:

To find the volume of the tall soup can, we use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder. We are given that the base area (A) of both cans is 30 cm², which allows us to find the radius before we can determine the height of the tall can.

First, we calculate the radius of the base using the formula for the area of a circle: A = πr². Thus, r = √(A/π). Substituting the given area into the formula, we get:

r = √(30 cm²/π)

Next, to find the height of the regular can, we rearrange the volume formula to h = V/(πr²) and substitute the known volume (270 cm³) and the radius we just calculated.

Finally, since the tall can is 2 cm taller than the regular can, we add 2 cm to the height of the regular can to find the height of the tall can, then calculate its volume using the adjusted height.

Answer 2

So first we need to solve for the height of the regular can. To do this you just take 30x = 270 and we find that the height will be 9 cm. Then we will add 2 to that which gets 11 cm. Then multiply that by the 30 cm^2. 30(11) = 330 cm^3.