The problem asks to determine whether to use lateral area (LA), surface area (SA), or volume (V) for each of the following situations: * The amount of cardboard in a paper towel roll tube. * The amount of water in a fishtank. * The amount of tin to form a soup can. And then, the problem asks to find the area of the label if it has a diameter of 4 inches and a height of 6 inches, and round to the nearest tenth.

1. Problem Description

The problem asks to determine whether to use lateral area (LA), surface area (SA), or volume (V) for each of the following situations:

* The amount of cardboard in a paper towel roll tube.

* The amount of water in a fishtank.

* The amount of tin to form a soup can.

And then, the problem asks to find the area of the label if it has a diameter of 4 inches and a height of 6 inches, and round to the nearest tenth.

2. Solution Steps

* The amount of cardboard in a paper towel roll tube: Since we're dealing with the material needed to construct the tube (the curved surface), we need the surface area. But since the ends are open, we need the lateral area.

* The amount of water in a fishtank: Since water fills the space inside the fishtank, we need the volume.

* The amount of tin to form a soup can: Since we are dealing with the material needed to construct the can, we need the surface area of the can. But since a soup can needs the top, bottom and the sides, and the surface area already includes the top and the bottom, we need the surface area.

Now for the second part of the problem.

The paper needed for the label is only for the side of the can which is the lateral surface area.

The diameter is 4 inches, so the radius $r$ is $4/2 = 2$ inches.

The height is 6 inches.

The lateral surface area of a cylinder is given by:

$LA = 2\pi r h$

Plugging in the values $r = 2$ and $h = 6$:

$LA = 2\pi (2)(6)$

$LA = 24\pi$

$LA \approx 24 \times 3.14159$

$LA \approx 75.398$

Rounding to the nearest tenth, we get $75.4$.

3. Final Answer

LA for the cardboard in a paper towel roll tube.

V for the amount of water in a fishtank.

SA for the amount of tin to form a soup can.

$75.4$ square inches are needed for the label.